Mathematical logic Books
Cambridge University Press LMS 189 Locally Presentable London Mathematical
Book SynopsisThe concepts of a locally presentable category and an accessible category have turned out to be useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students. Firstly the properties of l-presentable objects, locally l-presentable categories, and l-accessible categories are discussed in detail, and the equivalence of accessible and sketchable categories is proved. The authors go on to study categories of algebras and prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapters they treat some topics in model theory and some set theoretical aspects. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.Trade Review"...the authors have taken the indicated material, organized it effectively, written a very lucid, readable development of it in 280 pages, and added helpful historical remarks to each chapter and a brief appendix on large cardinals. There are some novel results...most notably a significant improvement of the Gabriel-Ulmer theorem on "local generation" of locally presentable categories." J.R. Isbell, Mathematical ReviewsTable of ContentsPreliminaries; 1. Locally presentable categories; 2. Accessible categories; 3. Algebraic categories; 4. Injectivity classes; 5. Categories of models; 6. Vopenka's principle; Appendix: Large cardinals; Open problems.
£87.99
Cambridge University Press Categories for Types
Book SynopsisThis textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories.Trade Review"A well-organized introduction to categorical methods of lambda calculus...The individual topics are treated in a uniform, balanced style from introduction, syntax, to categorical models and categorical-type theory correspondence." Jiri Adamek, Mathematical ReviewsTable of Contents1. Order, lattices and domains; 2. Basic category theory; 3. Algebraic type theory; 4. Functional type theory; 5. Polymorphic functional type theory; 6. Higher order polymorphism.
£120.00
Cambridge University Press Bounded Arithmetic Propositional Logic and Complexity Theory 60 Encyclopedia of Mathematics and its Applications Series Number 60
Book SynopsisThis book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics andTrade Review'This interesting book provides a brisk account of current research in bounded arithmetic and the complexity of propositional logic.' Mathematika'It can be strongly recommended especially to mathematicians and computer scientists working in the field and to graduate students.' European Mathematical Society NewsletterTable of Contents1. Introduction; 2. Preliminaries; 3. Basic complexity theory; 4. Basic propositional logic; 5. Basic bounded arithmetic; 6. Definability of computations; 7. Witnessing theorems; 8. Definability and witnessing in second order theories; 9. Translations of arithmetic formulas; 10. Finite axiomatizability problem; 11. Direct independence proofs; 12. Bounds for constant-depth Frege systems; 13. Bounds for Frege and extended Frege systems; 14. Hard tautologies and optimal proof systems; 15. Strength of bounded arithmetic; References; Index.
£122.55
Cambridge University Press Categories for Types Cambridge Mathematical Textbooks
Book SynopsisThis textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory. which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specialising in category theory.Trade Review"A well-organized introduction to categorical methods of lambda calculus...The individual topics are treated in a uniform, balanced style from introduction, syntax, to categorical models and categorical-type theory correspondence." Jiri Adamek, Mathematical ReviewsTable of Contents1. Order, lattices and domains; 2. Basic category theory; 3. Algebraic type theory; 4. Functional type theory; 5. Polymorphic functional type theory; 6. Higher order polymorphism.
£62.99
Cambridge University Press Semimodular Lattices Theory and Applications 73 Encyclopedia of Mathematics and its Applications Series Number 73
Book SynopsisIn Semimodular Lattices: Theory and Applications Manfred Stern uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. He focuses on the important theory of semimodularity, its many ramifications, and its applications in discrete mathematics, combinatorics, and algebra. The book surveys and analyzes Garrett Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and it presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. The author also deals with lattices that are 'close' to semimodularity or can be combined with semimodularity, e.g. supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book invaluable.Trade Review'Researchers working in lattice theory will surely welcome this excellent and up-to-date reference book.' Acta. Sci. Math.'I recommend the book highly to all interested readers, both experts and non-experts.' Stefan E. Schmidt, Bulletin of the London Mathematical Society'… a very well organized book … a pleasure to read … will certainly become a standard source.' Horst Szambien, Zentralblatt MATHTable of ContentsPreface; 1. From Boolean algebras to semimodular lattices; 2. M-symmetric lattices; 3. Conditions related to semimodularity, 0-conditions and disjointness properties; 4. Supersolvable and admissible lattices, consistent and strong lattices; 5. The covering graph; 6. Semimodular lattices of finite length; 7. Local distributivity; 8. Local modularity; 9. Congruence semimodularity; Master reference list; Table of notation; Index.
£125.00
Cambridge University Press The Logical Status of Diagrams
Book SynopsisDiagrams are widely used in reasoning about problems in physics, mathematics and logic, but have traditionally been considered to be only heuristic tools and not valid elements of mathematical proofs. This book challenges this prejudice against visualisation in the history of logic and mathematics and provides a formal foundation for work on natural reasoning in a visual mode.Trade Review"I will conclude by offering general praise for a work that really does deserve praise. Even more, it deserves to be read by those mathematicians and logicians who adhere to the general prejudice against diagrams. Shin has gone much farther than anyone in showing how a diagrammatic system can hold its own as a medium for reasoning....this book is clear and convincing....Shin's mastery and manipulation of her technical tools is always thorough and lucid. All in all, this is a very impressive, valuable piece of work." Modern Logic"The book is refreshing in its clarity and modesty, and in its regular return to historial precedents. It will give welcome reassurance to all those logicians for whom pictures seem indisputably the simplest way for the mind to comprehend syllogistic reasoning." M. Schiff, Choice"...The author's style is nice, very precise and approachable. The soundness and completeness of Venn systems provide a legitimate reason why logicians should be interested in nonlinguistic representation systems. Undoubtedly, this will be one of the rare inspiring sources motivating others to work in the field of visual representation systems." Branislav Boricic, Mathematical Reviews"Shin has shown that sysytems of diagrams can be developed that precisley parallel axiomatic formal systems for monadic predicate logic....Shin correctly points out what diagram systems and verbal systems can both do...that realistic pictures...can't." Phillip L. Peterson, Philosophy in ReviewTable of ContentsAcknowledgements; 1. Introduction; 2. Preliminaries; 3. Venn-I; 4. Venn-II; 5. Venn-II and L0; 6. Diagrammatic versus linguistic representation; 7. Conclusion; Appendix; References; Index.
£111.00
Cambridge University Press First Steps in Modal Logic
Book SynopsisThis is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory.Trade Review"This text should appeal to anyone with an interest in model logic...an attractive choice for self-study." J.M. Plotkin, Mathematical Reviews"...offers a distinctive viewpoint and is easy to learn from." D.V. Feldman, ChoiceTable of ContentsIntroduction; Acknowledgements; Part I. Preliminaries: 1. Survey of propositional logic; 2. The modal language; Part II. Transition Structures and Semantics: 3. Labelled transition structures; 4. Valuation and satisfaction; 5. Correspondence theory; 6. The general confluence result; Part III. Proof Theory and Completeness: 7. Some consequence relations; 8. Standard formal systems; 9. The general completeness result; 10. Kripke-completeness; Part IV. Model Constructions: 11. Bismulations; 12. Filtrations; 13. The finite model property; Part V. More Advanced Material: 14. SLL logic; 15. Löb logic; 16. Canonicity without the fmp; 17. Transition structures aren't enough; Part VI. Two Appendices: Bibliography.
£91.99
Cambridge University Press Basic Simple Type Theory 42 Cambridge Tracts in Theoretical Computer Science Series Number 42
Book SynopsisType theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for compTrade Review"This is an excellent introduction to type theory. It doesn't bog the reader down in any of the messy details of the proofs and yet it provides many of the most interesting results in the field....Overall, it is a great book for someone who wants to get his feet wet in type theory, but doesn't want to get in over his head." Sigact News"...the book makes useful and stimulating reading and it will be an essential tool for computer scientists working in type theory and related areas." Mathematical ReviewsThe proofs in this book are given in great detail, and still the author succeeds in writing the book in a clear but not too technical style. It is easy and pleasurable to read this book." Journal of Symbolic LogicTable of ContentsIntroduction; 1. The type-free λ-calculus; 2. Assigning types to terms; 3. The principal-type algorithm; 4. Type assignment with equality; 5. A version using typed terms; 6. The correspondence with implication; 7. The converse principal-type algorithm; 8. Counting a type's inhabitants; 9. Technical details; Answers to starred exercises; Bibliography; Table of principal types; Index.
£96.99
Cambridge University Press The Logic of Provability
Book SynopsisThis book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency (1979). Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency.Trade Review"The book contains an excellent combination of values: noble subject, fresh key results, and the gentle, friendly style of the author. It can be recommended as a textbook, as a handbook, or simply as high quality reading in logic." Sergei N. Artemov, Journal of Symbolic Logic"I found it lively, lucid, and informative...Boolos' style of writing is unusually kind to the reader. When an argument becomes tricky, he breaks it down into a lot of small steps, showing the reader in detail just how to proceed. A result is that the book is remarkably easy to read." Vann McGee, Rutgers UniversityTable of Contents1. GL and other systems of propositional modal logic; 2. Peano arithmetic; 3. The box as Bew(x); 4. Semantics for GL and other modal logics; 5. Completeness and decidability of GL and K, K4, T, B, S4, and S5; 6. Canonical models; 7. On GL; 8. The fixed point theorem; 9. The arithmetical completeness theorems for GL and GLS; 10. Trees for GL; 11. An incomplete system of modal logic; 12. An S4 -preserving proof-theoretical treatment of modality; 13. Modal logic within set theory; 14. Modal logic within analysis; 15. The joint provability logic of consistency and w-consistency; 16. On GLB: the fixed point theorem, letterless sentences, and analysis; 18. Quantified provability logic with one one-place predicate letter; Notes; Bibliography; Index.
£36.17
Cambridge University Press Proofs and Computations Perspectives in Logic
Book SynopsisDriven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and GÃdel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Î11âCA0. Ordinal analysis and the (SchwichtenbergâWainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Î11âCA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connTrade Review"Written by two leading practitioners in the area of formal logic, the book provides a panoramic view of the topic. This reference volume is a must for the bookshelf of every practitioner of formal logic and computer science." Prahladavaradan Sampath, Computing ReviewsTable of ContentsPreface; Preliminaries; Part I. Basic Proof Theory and Computability: 1. Logic; 2. Recursion theory; 3. Godel's theorems; Part II. Provable Recursion in Classical Systems: 4. The provably recursive functions of arithmetic; 5. Accessible recursive functions, ID<ω and Π11–CA0; Part III. Constructive Logic and Complexity: 6. Computability in higher types; 7. Extracting computational content from proofs; 8. Linear two-sorted arithmetic; Bibliography; Index.
£71.99
Cambridge University Press Models and Games
Book SynopsisThis gentle introduction makes extensive use of three important games in logic: the semantic game, the Ehrenfeucht-Fraisse game and the model existence game. Over 500 exercises are included and instructors will appreciate the game-theoretical presentation of basic materials as well as more advanced applications.Trade Review'The book can be used for reference purposes, as well as for teaching and self-study at the graduate level. It is a welcome addition to the literature on game-theoretic model theory.' Daniele Mundici, Zentralblatt MATH'… an interesting book that, while written by a logician, has lots of things to offer to computer scientists with theoretical inclinations.' Panos Rondogiannis, Theory and Practice of Logic Programming'… original and very ambitious … covers a remarkable amount of material, much in the main text and even more in over 500 exercises.' The Mathematical IntelligencerTable of ContentsPreface; 1. Introduction; 2. Preliminaries and notation; 3. Games; 4. Graphs; 5. Models; 6. First order logic; 7. Infinitary logic; 8. Model theory of infinitary logic; 9. Stronger infinitary logics; 10. Generalized quantifiers; References; Index.
£64.99
Cambridge University Press Logic Induction and Sets London Mathematical Society Student Texts
Book SynopsisThis is an introduction to logic and the axiomatization of set theory from a unique standpoint. Philosophical considerations, which are often ignored or treated casually, are here given careful consideration, and furthermore the author places the notion of inductively defined sets (recursive datatypes) at the centre of his exposition resulting in a treatment of well established topics that is fresh and insightful. The presentation is engaging, but always great care is taken to illustrate difficult points. Understanding is also aided by the inclusion of many exercises. Little previous knowledge of logic is required of the reader, and only a background of standard undergraduate mathematics is assumed.Trade Review'This is a remarkable book, presenting an introduction to mathematical logic and axiomatic set theory from a unified standpoint … also eminently suitable for self-study by mature mathematicians who wish to acquire a well-balanced and deeper knowledge of a field that is not part of their specialty … The author's presentation is a model of clarity, and much of the liveliness of a lecture has been preserved in the write-up. The various asides, cross-references, and care in motivating definitions and concepts all contribute to the value of the book as an instructional source … a treasure in its genre, to be highly recommended by the reviewer.' MathSciNet'… a real sense of freshness and vitality … I found this a very readable and stimulating book. Forster writes with an agreeably light touch and a whimsical sense of fun and his use of rectypes as a leitmotiv is both innovative and inspired.' The Mathematical Gazette'The author's philosophical training leads him to accompany many definitions with lengthy reflexions which add interest and enliven the book.' MathematikaTable of Contents1. Definitions and notations; 2. Recursive datatypes; 3. Partially ordered sets; 4. Propositional calculus; 5. Predicate calculus; 6. Computable functions; 7. Ordinals; 8. Set theory; 9. Answers to selected questions.
£48.24
Cambridge University Press Theories of Computability
Book SynopsisThis book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only 'the' theory of computability, but also a variety of other theories. Each topic is taken from the beginning and developed to a point at which the results can be appreciated.Trade Review"The author is extremely precise and meticulous, giving as much care to a proof that any context-free language can be generated by a grammar in Greibach normal form (GNF) as to a priority argument." Computing Reviews"...an excellent textbook for a beginning researcher who wants to familiarize himself/herself with several axiomatic frameworks for the theory of computability...I enjoyed the nuggets of wit spread throughout the book, providing a pleasant contrast to the abstract material." SIGACT News"Aiming readers at the frontier of research, the book has a point to make, and it makes it in an elegant and attractive way." Mathematical Reviews"The book, which has a list of about 200 references, is well indexed, well organized, and quite well written. But the strongest commendation is for its selection of material and its coherent organization." Siam ReviewTable of ContentsPreface; 1. Finite functions and relations; 2. Finite automata and their languages; 3. Grammars and their languages; 4. Computable functions and relations; References; Author index; Subject index; Math index.
£110.00
Cambridge University Press Computability Enumerability Unsolvability Directions in Recursion Theory 224 London Mathematical Society Lecture Note Series Series Number 224
Book SynopsisThe fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will make this volume an invaluable resource.Table of ContentsMinimal degrees below O' and the jump operator B. Cooper; Boolean algebras and ideals associated with the lattice of r.e. sets L. Harrington; Codable sets L. Harrington and R. Soare; Subrecursion theories A. Heaton and S. Wainer; An appraoch to lattice embaddings M. Lerman; A hierarchy of domains with totality, but without density D. Norman; Inductive inference P. Odifreddi; The discontinuity of the Slaman-Soare phenomenon X. YI; Recursive enumerability M. Arslanov; Resource bounded gereicity concepts K. Ambos-Spies; The Medvedev lattice of degrees of difficulty A. Sorbi; On the number of countable models II G. Sacks.
£50.99
Cambridge University Press Topology via Logic
Book SynopsisThis is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.Table of Contents1. Introduction; 2. Affirmative and refutative assertions; 3. Frames; 4. Frames as algebras; 5. Topology: the definitions; 6. New topologies for old; 7. Point logic; 8. Compactness; 9. Spectral algebraic locales; 10. Domain theory; 11. Power domains; 12. Spectra of rings; Bibliography.
£56.16
Cambridge University Press Metamaths Machines Godels Proof 38 Cambridge Tracts in Theoretical Computer Science Series Number 38
Book SynopsisMathematicians from Leibniz to Hilbert have sought to mechanise the verification of mathematical proofs. Developments arising out of GÃdel's proof of his incompleteness theorem showed that no computer program could automatically prove true all the theorems of mathematics. In practice, however, there are a number of sophisticated automated reasoning programs that are quite effective at checking mathematical proofs. Now in paperback, this book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including GÃdel's incompleteness theorem and the ChurchâRosser theorem. The computer verification using the BoyerâMoore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanisation of metamathematics itself has important implications for automated reasoning since metatheorems can be applied by labour-saving devices to simpliTable of Contents1. Introduction; 2. The statement of the incompleteness theorem; 3. Derived inference rules; 4. The representability of metatheory; 5. The undecidable sentence; 6. A mechanical proof of the Church–Rosser theorem; 7. Conclusions.
£42.99
Cambridge University Press LMS 244 Model Theory Grps Auto Grp London Mathematical Society Lecture Note Series Series Number 244
Book SynopsisThis volume surveys recent interactions between model theory and other branches of mathematics, notably group theory. Beginning with an introductory chapter describing relevant background material, the book contains contributions from many leading international figures in this area. Topics described include automorphism groups of algebraically closed fields, the model theory of pseudo-finite fields and applications to the subgroup structure of finite Chevalley groups. Model theory of modules, and aspects of model theory of various classes of groups, including free groups, are also discussed. The book also contains the first comprehensive survey of finite covers. Many new proofs and simplifications of recent results are presented and the articles contain many open problems. This book will be a suitable guide for graduate students and a useful reference for researchers working in model theory and algebra.Trade Review'The interesting articles range from purely group theoretic ones to mainly model theoretic ones … and reflect impressively the prolific interaction between these two fields.' Monatshefte für MathematikTable of ContentsPreface; 1. Introduction; 2. Finite covers; 3. Definable subgroups of algebraic groups over pseudo-finite fields; 4. Groups in pseudo-finite fields; 5. The groups of automorphisms of the field of complex numbers leaving fixed the algebraic numbers are simple; 6. The automorphism groups of the field of complex numbers are complete; 7. The algebra of an age; 8. Elimination of inverses in groups; 9. Model-theoretic properties of polycyclic-by-finite groups; 10. Non-standard free groups; 11. Finitely generated subgroups of the free Z(t)-group on two generators; 12. Rings of definable scalars and biendomorphism rings; 13. Recent results on simple first-order theories.
£50.99
Cambridge University Press Set Theory 48 London Mathematical Society Student Texts Series Number 48
Book SynopsisThis is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems.Trade Review'This is a classic introduction to set theory …'. L'Enseignement Mathématique'Give this book fifteen minutes attention - you will find that you must buy it! European Maths Society JournalTable of ContentsPart I. Introduction to Set Theory: 1. Notation, conventions; 2. Definition of equivalence. The concept of cardinality. The axiom of choice; 3. Countable cardinal, continuum cardinal; 4. Comparison of cardinals; 5. Operations with sets and cardinals; 6. Examples; 7. Ordered sets. Order types. Ordinals; 8. Properties of well-ordered sets. Good sets. The ordinal operation; 9. Transfinite induction and recursion; 10. Definition of the cardinality operation. Properties of cardinalities. The confinality operation; 11. Properties of the power operation; Appendix. An axiomatic development of set theory; Part II. Topics in Combinatorial Set Theory: 12. Stationary sets; 13. Delta-systems; 14. Ramsey's theorem and its generalizations. Partition calculus; 15. Inaccessible cardinals. Mahlo cardinals; 16. Measurable cardinals; 17. Real-valued measurable cardinals, saturated ideas; 18. Weakly compact and Ramsey cardinals; 19. Set mappings; 20. The square-bracket symbol. Strengthenings of the Ramsey counterexamples; 21. Properties of the power operation; 22. Powers of singular cardinals. Shelah's theorem.
£123.00
Cambridge University Press Set Theory for the Working Mathematician 39 London Mathematical Society Student Texts Series Number 39
Book SynopsisThis text concentrates on the typical methods of modern set theory: transfinite induction, Zorn's Lemma, the Continuum Hypothesis, Martin's Axiom, the Diamond Principle and elements of forcing. It supplies students and researchers with the tools most applicable to other areas of pure mathematics, such as abstract geometry, real analysis, topology, and algebra.Trade Review' … the author has produced a very valuable resource for the working mathematician. Postgraduates and established researchers in many (perhaps all) areas of mathematics will benefit from reading it.' Ian Tweddle, Proceedings of the Edinburgh Mathematical SocietyTable of ContentsPart I. Basics of Set Theory: 1. Axiomatic set theory; 2. Relations, functions and Cartesian product; 3. Natural, integer and real numbers; Part II. Fundamental Tools of Set Theory: 4. Well orderings and transfinite induction; 5. Cardinal numbers; Part III. The Power of Recursive Definitions: 6. Subsets of Rn; 7. Strange real functions; Part IV. When Induction is Too Short: 8. Martin's axiom; 9. Forcing; Part V. Appendices: A. Axioms of set theory; B. Comments on forcing method; C. Notation.
£123.00
Cambridge University Press Set Theory for the Working Mathematician
Book SynopsisThis text concentrates on the typical methods of modern set theory: transfinite induction, Zorn's Lemma, the Continuum Hypothesis, Martin's Axiom, the Diamond Principle and elements of forcing. It supplies students and researchers with the tools most applicable to other areas of pure mathematics, such as abstract geometry, real analysis, topology, and algebra.Trade Review' … the author has produced a very valuable resource for the working mathematician. Postgraduates and established researchers in many (perhaps all) areas of mathematics will benefit from reading it.' Ian Tweddle, Proceedings of the Edinburgh Mathematical SocietyTable of ContentsPart I. Basics of Set Theory: 1. Axiomatic set theory; 2. Relations, functions and Cartesian product; 3. Natural, integer and real numbers; Part II. Fundamental Tools of Set Theory: 4. Well orderings and transfinite induction; 5. Cardinal numbers; Part III. The Power of Recursive Definitions: 6. Subsets of Rn; 7. Strange real functions; Part IV. When Induction is Too Short: 8. Martin's axiom; 9. Forcing; Part V. Appendices: A. Axioms of set theory; B. Comments on forcing method; C. Notation.
£45.99
Cambridge University Press LMSST 48 Set Theory London Mathematical Society Student Texts Series Number 48
Book SynopsisThis is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems.Trade Review'This is a classic introduction to set theory …'. L'Enseignement Mathématique'Give this book fifteen minutes attention - you will find that you must buy it! European Maths Society JournalTable of ContentsPart I. Introduction to Set Theory: 1. Notation, conventions; 2. Definition of equivalence. The concept of cardinality. The axiom of choice; 3. Countable cardinal, continuum cardinal; 4. Comparison of cardinals; 5. Operations with sets and cardinals; 6. Examples; 7. Ordered sets. Order types. Ordinals; 8. Properties of well-ordered sets. Good sets. The ordinal operation; 9. Transfinite induction and recursion; 10. Definition of the cardinality operation. Properties of cardinalities. The confinality operation; 11. Properties of the power operation; Appendix. An axiomatic development of set theory; Part II. Topics in Combinatorial Set Theory: 12. Stationary sets; 13. Delta-systems; 14. Ramsey's theorem and its generalizations. Partition calculus; 15. Inaccessible cardinals. Mahlo cardinals; 16. Measurable cardinals; 17. Real-valued measurable cardinals, saturated ideas; 18. Weakly compact and Ramsey cardinals; 19. Set mappings; 20. The square-bracket symbol. Strengthenings of the Ramsey counterexamples; 21. Properties of the power operation; 22. Powers of singular cardinals. Shelah's theorem.
£62.99
Cambridge University Press LMS 248 Tame Topology ominimal London Mathematical Society Lecture Note Series Series Number 248
Book SynopsisThese notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.Trade Review"...indispensable to any student or research interested in o-minimal structures. ...written with remarkable precision and clarity..." Bulletin of the AMS"This is an excellent textbook..." Bulletin of Symbolic LogicTable of Contents1. Some elementary results; 2. Semialgebraic sets; 3. Cell decomposition; 4. Definable invariants: Dimension and Euler characteristic; 5. The Vapnik–Chernovenkis property in o-minimal structures; 6. Point-set topology in o-minimal structures; 7. Smoothness; 8. Triangulation; 9. Trivialization; 10. Definable spaces and quotients.
£61.99
Cambridge University Press Stable Groups 240 London Mathematical Society Lecture Note Series Series Number 240
Book SynopsisIn this book, the general theory of stable groups is developed from the beginning, concentrating on the model- and group-theoretic aspects. It brings together the various extensions of the original finite rank theory under a unified perspective and provides a coherent exposition of the knowledge in the field.Trade Review' … a valuable addition to the model-theoretic literature'. Dugald MacPherson, Bulletin of the London Mathematical Society'This book presents the state-of-the-art of the field …' Zentralblatt für Mathematik und ihre Grenzgebiete'… an original contribution to the theory.' A. Baudisch, Niew Archief voor WiskundeTable of Contents1. Groups and goals; 2. Groups and generality; 3. Groups and genericity; 4. Groups and grandeur; 5. Groups and geometry; 6. Groups and grades; Bibliography.
£66.68
Cambridge University Press Automata Theory with Modern Applications
Book SynopsisRecent applications to bioscience have created a new audience for automata theory and formal languages. This is the only introduction to cover such applications. With over 350 exercises, many examples and illustrations, this is an ideal contemporary introduction for students; others, new to the field, will welcome it for self-learning.Trade Review'Anderson's book gives an excellent, clearly written account of automata theory.' SIAM ReviewTable of Contents1. Introduction; 2. Languages and codes; 3. Automata; 4. Grammars; 5. Turing machines; 6. A visual approach to formal languages; 7. From biopolymers to formal language theory; Bibliography; Index.
£52.20
Cambridge University Press Algorithmic Information Theory
Book SynopsisChaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gödel's incompleteness theorem, using an information theoretic approach based on the size of computer programs.Table of ContentsForeword; Preface; Figures; 1. Introduction; Part I. Formalisms for Computation: Register Machines, Exponential Diophantine Equations, and Pure LISP: 2. The arithmetization of register machines; 3. A version of Pure LISP; 4. The LISP interpreter EVAL; Part II. Program Size, Halting Probabilities, Randomness, and Metamathematics: 5. Conceptual development; 6. Program size; 7. Randomness; 8. Incompleteness; 9. Conclusion; Bibliography.
£47.99
Cambridge University Press Domains and LambdaCalculi 46 Cambridge Tracts in Theoretical Computer Science Series Number 46
Book SynopsisThis book describes the mathematical aspects of the semantics of programming languages. The main goals are to provide formal tools to assess the meaning of programming constructs in both a language-independent and a machine-independent way, and to prove properties about programs, such as whether they terminate, or whether their result is a solution of the problem they are supposed to solve. In order to achieve this the authors first present, in an elementary and unified way, the theory of certain topological spaces that have proved of use in the modelling of various families of typed lambda calculi considered as core programming languages and as meta-languages for denotational semantics. This theory is known as Domain Theory, and was founded as a subject by Scott and Plotkin. One of the main concerns is to establish links between mathematical structures and more syntactic approaches to semantics, often referred to as operational semantics, which is also described. This dual approach haTrade ReviewReview of the hardback: '… extremely useful as a reference for classical results and techniques in general domain theory, very balanced in the treatment of mathematical properties of domains and their operational motivations and applications, and always deep in the choice of topics and in unravelling the connections between them.' Felice Cardone, Science of Computer ProgrammingReview of the hardback: 'This is an excellent, thorough monograph … a rich and comprehensive source of information, it is very useful as a reference to classical results in domain theory and lambda calculus.' Paula G. Severi, Zentralblatt MATHTable of ContentsPreface; Notation; 1. Continuity and computability; 2. Syntactic theory of λ-calculus; 3. D∞ models and intersection types; 4. Interpretation of λ-calculi in CCC's; 5. CCC's of algebraic dcpo's; 6. The language PCF; 7. Domain equations; 8. Values and computations; 9. Powerdomains; 10. Stone duality; 11. Dependent and second order types; 12. Stability; 13. Towards linear logic; 14. Sequentiality; 15. Domains and realizability; 16. Functions and processes; Appendix 1: summary of recursion theory; Appendix 2: summary of category theory; References and bibliography; Index.
£135.00
Cambridge University Press Principia Mathematica to 56
Book SynopsisThe great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part 1 (in which the logical properties of propositions, propositional functions, classes and relations are established); section 6 of Part 2 (dealing with unit classes and couples); and Appendices A and B (which give further developments of the argument on the theory of deduction anTable of ContentsPart I. Mathematical Logic: 1. The theory of deduction; 2. Theory of apparent variables; 3. Classes and relations; 4. Logic or relations; 5. Products and sums of classes; Part II. Prolegomena to Cardinal Arithmetic: 6. Unit classes and couples; Appendix A. Type theory of dependant variables and propositions containing apparent variables; Appendix B. Truth functions and others.
£95.99
Cambridge University Press Sets and Proofs 258 London Mathematical Society Lecture Note Series Series Number 258
Book SynopsisThis book and its sister volume, Models and Computability, provide readers with a comprehensive guide to the mathematical logic. All the authors are leaders in their fields and are drawn from invited speakers at 'Logic Colloquium '97' (the major international meeting of the Association of Symbolic Logic).Trade Review'All the authors are leaders in their fields, some articles pushing forward the technical boundaries of the subject, others providing readable and authoritative overviews of particular important topics … a number of papers can be expected to become classics, essential to any good library (individual or institutional).' Extrait de L'Enseignement MathématiqueTable of Contents1. An introduction to finitary analyses of proof figures T. Arai; 2. What mathematical truth could not be - II P. Benacerraf; 3. Proof search in constructive logics R. Dyckhoff and L. F. Pinto; 4. David's trick S. D. Friedman; 5. A semantical calculus for intuitionistic propositional logic J. Hudelmaier; 6. An iteration model violating the singular cardinals hypothesis P. Koepke; 7. An introduction to core model theory B. Löwe and J. R. Steel; 8. Games of countable length I. Neeman; 9. On the complexity of the propositional calculus P. Pudlak; 10. The realm of ordinal analysis M. Rathjen; 11. Covering properties of core models E. Schimmerling; 12. Ordinal systems A. Setzer; 13. Polish group topologies S. Solecki; 14. Forcing closed unbounded subsets of Nw+1 M. C. Stanley; 15. First steps into metapredicativity in explicit mathematics T. Strahm; 16. What makes a (pointwise) subrecursive hierarchy slow growing? A. Weiermann; 17. Minimality arguments for infinite time Turing degrees P. D. Welch.
£61.75
Cambridge University Press Models and Computability 259 London Mathematical Society Lecture Note Series Series Number 259
Book SynopsisThis book and its sister volume, Sets and Proofs, provide readers with a comprehensive guide to the current state of mathematical logic. All the authors are leaders in their fields and are drawn from invited speakers at 'Logic Colloquium '97' (the major international meeting of the Association of Symbolic Logic).Trade Review' … will prove an invaluable and unique resource for specialists, post-graduate researchers, and the informed and interested nonspecialist.' Extrait de L'Enseignement MathématiqueTable of Contents1. Continuous functionals of dependent and transfinite types U. Berger; 2. Degree-theoretic aspects of computably enumerable reals C. S. Claude, R. Coles, P. H. Hertling and B. Khoussainov; 3. Simplicity and independence for pseudo-algebraically closed fields Z. Chatzidakis; 4. Clockwork or Turing universe? - remarks on causal determinism and computability S. B. Cooper; 5. A techniques-oriented survey of bounded queries W. Gasarch and F. Stephan; 6. Relative categoricity in abelian groups W. A. Hodges; 7. Computability and complexity revisited N. D. Jones; 8. Effective model theory: the number of models and their complexity B. Khoussainov and R. A. Shore; 9. A survey on canonical bases in simple theories B. Kim; 10. True approximations and models of arithmetic J. F. Knight; 11. On the topological stability conjecture L. Newelski; 12. A mahlo-universe of effective domains with totality D. Normann; 13. Logic and decision making D. E. Over; 14. The sheaf of locally definable scalars over a ring M. Y. Prest; 15. Human styles of quantificational reasoning L. J. Rips; 16. Recursion theoretic memories 1954–1978 G. E. Sacks; 17. Fields definable in simple groups K. Tent; 18. A combinatory algebra for sequential functionals of finite type J. Van Oosten; 19. Model theory of analytic and smooth functions A. J. Wilkie.
£61.60
Cambridge University Press Proofs and Confirmations
Book SynopsisAn introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses.Trade Review'Proofs and Confirmations is one of the most brilliant examples of mathematical exposition that I have encountered, in many years of reading the same. This is not for the faint-hearted, nor is Proofs and Confirmations a book that can be read in an easy chair, like a novel; it demands active participation by the reader. But Bressoud rewards such readers with a panorama of combinatorics today and with renewed awe at the human ability to penetrate the deeply hidden mysteries of pure mathematics.' Herbert S. Wilf, Science'The unexpected twists and turns will hardly be matched in any novel - this book allows us all to share in the excitement … a brilliant book.' Alun O. Morris'I strongly recommend the book as an account of a remarkable mathematical development.' P. J. Cameron, Proceedings of the Edinburgh Mathematical Society'This is an excellent book which can be recommended without hesitation, not only to specialists in the field, but to any mathematician with time to read something interesting and nicely written.' EMSTable of Contents1. The conjecture; 2. Fundamental structures; 3. Lattice paths and plane partitions; 4. Symmetric functions; 5. Hypergeometric series; 6. Explorations; 7. Square ice.
£44.88
Cambridge University Press Dependence Logic A New Approach To Independence Friendly Logic
Book SynopsisDependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka's independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic.Trade Review"The material is written in a very friendly way. Definitions of the majority of the important notions are preceded by explanations of the ideas. Moreover, the book contains more than 200 exercises, many of which have a solution at the end of the book. This makes it easier to read the book and understand its material. The book could definitely be interesting to a wide spectrum of mathematicians, philosophers and computer scientists." - Michael Krynicki, Mathematical ReviewsTable of ContentsPreface; 1. Introduction; 2. Preliminaries; 3. Dependence logic; 4. Examples; 5. Game theoretic semantics; 6. Model Theory; 7. Complexity; 8. Team logic; 9. Solutions to selected exercises by Ville Nurmi; References; Index.
£59.11
Cambridge University Press An Introduction to ManyValued and Fuzzy Logic Semantics Algebras and Derivation Systems
Book SynopsisProfessor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, GÃdel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.Trade Review"Bergmann has done an excellent job...Highly recommended." R. Bharath, Northern Michigan University, ChoiceTable of ContentsPreface; 1. Introduction; 2. Review of classical propositional logic; 3. Review of classical first-order logic; 4. Alternative semantics for truth-values and truth-functions; 5. Three-valued propositional logics: semantics; 6. Derivation systems for three-valued propositional logic; 7. Three-valued first-order logics: semantics; 8. Derivation systems for three-valued first-order logics; 9. Alternative semantics for three-valued systems; 10. The principle of charity reconsidered and a new problem of the fringe; 11. Fuzzy propositional logics: semantics; 12. Fuzzy algebras; 13. Derivational systems for fuzzy propositional logics; 14. Fuzzy first-order logics: semantics; 15. Derivation systems for fuzzy first-order logics; 16. Extensions of fuzziness; 17. Fuzzy membership functions.
£53.99
Cambridge University Press The Mathematics of Logic A Guide to Completeness Theorems and Their Applications
Book SynopsisThis undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with KÃnig's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theoTrade Review"Kaye (pure mathematics, U. of Birmingham) gives undergraduate and first-year graduates key materials for a first course in logic, including a full mathematical account of the Completeness Theorem for first-order logic. As he builds a series of systems increasing in complexity, and proving and discussing the Completeness Theorem for each, Kaye keeps unfamiliar terminology to a minimum and provides proofs of all the required set theoretical results. He covers K<:o>nig's Lemma (including two ways of looking at mathematics), posets and maximal elements (including order), formal systems (including post systems and compatibility as bonuses), deduction in posets (including proving statements about a poset), Boolean algebras, propositional logic (including a system for proof about propositions), valuations (including semantics for propositional logic), filters and ideals (including the algebraic theory of Boolean algebras), first-order logic, completeness and compactness, model theory (including countable models) and nonstandard analysis (including infinitesimal numbers)." --Book NewsTable of ContentsPreface; How to read this book; 1. König's lemma; 2. Posets and maximal elements; 3. Formal systems; 4. Deductions in posets; 5. Boolean algebras; 6. Propositional logic; 7. Valuations; 8. Filters and ideals; 9. First-order logic; 10. Completeness and compactness; 11. Model theory; 12. Nonstandard analysis; Bibliography; Index.
£47.26
Cambridge University Press Alfred Tarski Life and Logic
Book SynopsisAlfred Tarski, one of the greatest logicians of all time, is widely thought of as 'the man who defined truth'. His work on the concepts of truth and logical consequence are cornerstones of modern logic, influencing developments in mathematics, philosophy, linguistics, and computer science. Tarski was a charismatic teacher and zealous promoter of his view of logic as the foundation of all rational thought, a bon vivant and a womanizer, who played the 'great man' to the hilt. A fortuitous trip to the United States at the outbreak of World War II saved his life and turned his career around, even while it separated him from his family for years. From the cafÃs of Warsaw and Vienna to the mountains and deserts of California, this first full-length biography places Tarski in the social, intellectual, and historical context of his times and presents a frank, vivid picture of a personally and professionally passionate man - interlaced with an account of his major scientific achievements.Trade Review'The Fefermans' biography is an enthralling success story of a self-confident, enterprising, untiring, and entrepreneurial scientist, and a rich and scrupulous account of the numerous achievements accomplished by this powerful logician and his colleagues in philosophy of logic, semantics, set theory, decision procedures, universal algebra, algebraic logic, axiomatic geometry, topology, and model theory.' Hourya Benis Sinaceur, Notices of the AMS'A chain smoker, a heavy drinker, a frequent user of 'speed', a relentless womaniser, and a man of Napoleonic self-regard and worldly ambition. This is not how one pictures an eminent Professor of Logic. And yet, this is how the great logician, Alfred Tarski, emerges from this marvellous biography. The Fefermans, of course, are uniquely qualified to lead the reader through the intricacies of Tarski's work, which they do very engagingly and with great expository skill. Tarski's colourful personality is conveyed with prose that is economical, superbly readable and extremely vivid, and the whole book is a joy to read.' Ray Monk, author of biographies of Wittgenstein and Russell'The story of a remarkable Polish mathematician called Alfred Tarski, who fled the Nazi persecution, came to the United States, and single-handedly turned the Mathematics Department of the University of California at Berkeley into the world center for the study of logic. Anita and Sol Feferman's captivating biography pulls no punches, describing his womanizing and his drug use along with his mathematical achievements.' Keith Devlin, Stanford University and author of Goodbye Descartes: The End of Logic and the Search for a New Cosmology of the Mind'It was a great pleasure to absorb myself in this prodigious work. The heritage of Tarski's Poland is just one of the many themes which the authors develop with sympathy, yet unflinchingly reveal as heavy with conflicts of identity and loyalty. I am amazed at how much they got out of pre-war Poland and at the way they unfold so much of the interior 'logic world' in the course of telling the story. An expert 'interlude' is devoted to explaining the problem of formalising truth, the central spring of Tarski's creative work.' Andrew Hodges, author of Alan Turing: The Enigma'Here we have a vivid portrait of Alfred Tarski as a man of enormous energy and focus, devoted to logic, women and slivovitz, entirely lacking in self-doubt, and ambivalent about his Jewish heritage. The Fefermans provide a richly textured account of the cultural, intellectual, and political worlds in which Tarski lived -- first in interwar Poland and then in Berkeley, where he built his logic empire. They also draw highly individualized portraits of the many people who figured in Tarski's life and career. The work that made Tarski one of logic's giants is lucidly explained in a series of compact interludes. This is a wonderful book on many levels.' Elliot Sober, University of Wisconsin, MadisonTable of Contents1. The two Tarskis; 2. Independence and university; Interlude I. The Banach-Tarski paradox, set theory and the axiom of choice; 3. Polot! The Polish attribute; Interlude II. The completeness and decidability of algebra and geometry; 4. A wider sphere of influence; Interlude III. Truth and definability; 5. How the 'Unity of Science' saved Tarski's life; 6. Berkeley is so far from Princeton; 7. Building a school; Interlude IV. The publication campaigns; 8 'Papa Tarski' and his students; 9. Three meetings and two departures; 10. Logic and methodology, center stage; 11. Heydays; Interlude V. Model theory and the 1963 symposium; 12. Around the world; 13. Los Angeles and Berkeley; Interlude VI. Algebras of logic; 14. A decade of honors; 15. The last times.
£32.42
Cambridge University Press A Course in Model Theory
Book SynopsisThis concise introduction takes the reader from standard notions to more advanced topics. It introduces the classic results, as well as more recent developments in this vibrant area of mathematical logic. Many worked examples and exercises make the book a useful resource for graduate students as well as researchers.Trade Review'The book is very well written and a pleasure to read.' Tim Netzer, Zentralblatt MATHTable of ContentsPreface; 1. The basics; 2. Elementary extensions and compactness; 3. Quantifier elimination; 4. Countable models; 5. Aleph-1-categorical theories; 6. Morley rank; 7. Simple theories; 8. Stable theories; 9. Prime extensions; 10. The fine structure of 1-categorical theories; A. Set theory; B. Fields; C. Combinatorics; D. Solutions of exercises; Bibliography; Index.
£54.99
Cambridge University Press Alfred Tarski Life and Logic
Book SynopsisAlfred Tarski, one of the greatest logicians of all time, is widely thought of as 'the man who defined truth'. His work on the concepts of truth and logical consequence are cornerstones of modern logic, influencing developments in mathematics, philosophy, linguistics, and computer science. Tarski was a charismatic teacher and zealous promoter of his view of logic as the foundation of all rational thought, a bon vivant and a womanizer, who played the 'great man' to the hilt. A fortuitous trip to the United States at the outbreak of World War II saved his life and turned his career around, even while it separated him from his family for years. From the cafÃs of Warsaw and Vienna to the mountains and deserts of California, this first full-length biography places Tarski in the social, intellectual, and historical context of his times and presents a frank, vivid picture of a personally and professionally passionate man - interlaced with an account of his major scientific achievements.Trade Review'The Fefermans' biography is an enthralling success story of a self-confident, enterprising, untiring, and entrepreneurial scientist, and a rich and scrupulous account of the numerous achievements accomplished by this powerful logician and his colleagues in philosophy of logic, semantics, set theory, decision procedures, universal algebra, algebraic logic, axiomatic geometry, topology, and model theory.' Hourya Benis Sinaceur, Notices of the AMS'A chain smoker, a heavy drinker, a frequent user of 'speed', a relentless womaniser, and a man of Napoleonic self-regard and worldly ambition. This is not how one pictures an eminent Professor of Logic. And yet, this is how the great logician, Alfred Tarski, emerges from this marvellous biography. The Fefermans, of course, are uniquely qualified to lead the reader through the intricacies of Tarski's work, which they do very engagingly and with great expository skill. Tarski's colourful personality is conveyed with prose that is economical, superbly readable and extremely vivid, and the whole book is a joy to read.' Ray Monk, author of biographies of Wittgenstein and Russell'The story of a remarkable Polish mathematician called Alfred Tarski, who fled the Nazi persecution, came to the United States, and single-handedly turned the Mathematics Department of the University of California at Berkeley into the world center for the study of logic. Anita and Sol Feferman's captivating biography pulls no punches, describing his womanizing and his drug use along with his mathematical achievements.' Keith Devlin, Stanford University and author of Goodbye Descartes: The End of Logic and the Search for a New Cosmology of the Mind'It was a great pleasure to absorb myself in this prodigious work. The heritage of Tarski's Poland is just one of the many themes which the authors develop with sympathy, yet unflinchingly reveal as heavy with conflicts of identity and loyalty. I am amazed at how much they got out of pre-war Poland and at the way they unfold so much of the interior 'logic world' in the course of telling the story. An expert 'interlude' is devoted to explaining the problem of formalising truth, the central spring of Tarski's creative work.' Andrew Hodges, author of Alan Turing: The Enigma'Here we have a vivid portrait of Alfred Tarski as a man of enormous energy and focus, devoted to logic, women and slivovitz, entirely lacking in self-doubt, and ambivalent about his Jewish heritage. The Fefermans provide a richly textured account of the cultural, intellectual, and political worlds in which Tarski lived -- first in interwar Poland and then in Berkeley, where he built his logic empire. They also draw highly individualized portraits of the many people who figured in Tarski's life and career. The work that made Tarski one of logic's giants is lucidly explained in a series of compact interludes. This is a wonderful book on many levels.' Elliot Sober, University of Wisconsin, MadisonTable of Contents1. The two Tarskis; 2. Independence and university; Interlude I. The Banach-Tarski paradox, set theory and the axiom of choice; 3. Polot! The Polish attribute; Interlude II. The completeness and decidability of algebra and geometry; 4. A wider sphere of influence; Interlude III. Truth and definability; 5. How the 'Unity of Science' saved Tarski's life; 6. Berkeley is so far from Princeton; 7. Building a school; Interlude IV. The publication campaigns; 8 'Papa Tarski' and his students; 9. Three meetings and two departures; 10. Logic and methodology, center stage; 11. Heydays; Interlude V. Model theory and the 1963 symposium; 12. Around the world; 13. Los Angeles and Berkeley; Interlude VI. Algebras of logic; 14. A decade of honors; 15. The last times.
£117.00
Cambridge University Press Continuous Lattices and Domains 93 Encyclopedia of Mathematics and its Applications Series Number 93
Book SynopsisInformation content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. This authoritative and comprehensive account of the subject will be an essential handbook for all those working in the area.Trade Review'A highly recommendable handbook on a subject which links algebra and topology in a convincing and beautiful way.' H. Mitsch, Wien'Being written in an expository and almost self-contained way, the book can serve as a handbook for those working in the area as well as a student textbook.' EMS Newsletter'… this is the book for all those interested in the topic … I am pleased to recommend … this most authentic source of information on continuous lattices and domains.' Acta Scientiarum MathematicarumTable of ContentsPreface; Acknowledgements; Foreword; Introduction; 1. A primer on ordered sets and lattices; 2. Order theory of domains; 3. The Scott topology; 4. The Lawson Topology; 5. Morphisms and functors; 6. Spectral theory of continuous lattices; 7. Compact posets and semilattices; 8. Topological algebra and lattice theory: Applications; Bibliography; List of symbols; List of categories; Index.
£205.00
Cambridge University Press Rippling MetaLevel Guidance for Mathematical Reasoning 56 Cambridge Tracts in Theoretical Computer Science Series Number 56
Book SynopsisRippling is a radically new technique for the automation of mathematical reasoning. It is widely applicable whenever a goal is to be proved from one or more syntactically similar givens. It was originally developed for inductive proofs, where the goal was the induction conclusion and the givens were the induction hypotheses. It has proved to be applicable to a much wider class of tasks, from summing series via analysis to general equational reasoning. The application to induction has especially important practical implications in the building of dependable IT systems, and provides solutions to issues such as the problem of combinatorial explosion. Rippling is the first of many new search control techniques based on formula annotation; some additional annotated reasoning techniques are also described here. This systematic and comprehensive introduction to rippling, and to the wider subject of automated inductive theorem proving, will be welcomed by researchers and graduate students alikTable of ContentsPreface; 1. An introduction to rippling; 2. Varieties of rippling; 3. Productive use of failure; 4. A formal account of rippling; 5. The scope and limitations of rippling; 6. From rippling to a general methodology; 7. Conclusions; Appendix 1. An annotated calculus and a unification algorithm; Appendix 2. Definitions of functions used in this book; Bibliography; Index.
£111.13
Cambridge University Press Automata Theory with Modern Applications
Book SynopsisRecent applications to biomolecular science and DNA computing have created a new audience for automata theory and formal languages. This is the only introductory book to cover such applications. It begins with a clear and readily understood exposition of the fundamentals that assumes only a background in discrete mathematics. The first five chapters give a gentle but rigorous coverage of basic ideas as well as topics not found in other texts at this level, including codes, retracts and semiretracts. Chapter 6 introduces combinatorics on words and uses it to describe a visually inspired approach to languages. The final chapter explains recently-developed language theory coming from developments in bioscience and DNA computing. With over 350 exercises (for which solutions are available), many examples and illustrations, this text will make an ideal contemporary introduction for students; others, new to the field, will welcome it for self-learning.Trade Review'Anderson's book gives an excellent, clearly written account of automata theory.' SIAM ReviewTable of Contents1. Introduction; 2. Languages and codes; 3. Automata; 4. Grammars; 5. Turing machines; 6. A visual approach to formal languages; 7. From biopolymers to formal language theory; Bibliography; Index.
£80.00
Cambridge University Press An Introduction to NonClassical Logic
Book SynopsisThis revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues are explained.Trade Review'Priest's Introduction to Non-Classical Logic is my textbook of choice for introducing non-classical logic to undergraduates. It is unique in meeting two almost inconsistent aims. It gives the reader an introduction to a vast range of non-classical logics. No comparable textbook manages to cover modal logics, conditional logics, intuitionistic logic, relevant and paraconsistent logics and fuzzy logic with such clarity and accessibility. Amazingly, it is not merely a catalogue of different logical systems. The distinctive value of this Introduction is that it also tells a coherent story: Priest weaves together these different logics in the one narrative - the search for a logic of conditionals. With the publication of the second volume, this unique combination of breadth and coherence now covers much more ground, and the reader now has an expert guide to much more of the vast field of research in non-classical logics.' Greg Restall, The University of Melbourne'I've used your book (first edition, that is) for years now in my upper level philosophy of logic courses. It is easily the best introduction to non-classical logics. I especially like its coverage of conditionals, and the introduction to relevant logic. Over the years, your book has made my students come to appreciate the variety and scope that exists within in formal logic, I intend to use the new edition so as to carry similar investigations into first order theory.' Jeffry Pelletier, Simon Fraser University'Graham Priest's Introduction to Non-Classical Logic made this fascinating material on alternative logics accessible to my students for the very first time. The very welcome new edition extends the range of what is addressed to include important questions about quantification for modal logic, and the other systems as well.' Tony Roy, California State University, San Bernardino'The first edition of Graham Priest's Introduction to Non-Classical Logic turned out to be an extremely useful and well-written introductory guide to the vast and difficult to survey area of non-classical and philosophical logic. The substantially expanded second edition in two volumes is bound to become a standard reference.' Heinrich Wansing, Dresden University of Technology'Clear, self-contained, generously complete: this is bound to be the classic on non-classical logics for many years to come.' Achille Varzi, Columbia University'This is an excellent introductory book to modern non-classical logics, fully accessible to non-professionals, and useful to professionals too. I have used part of its content in teaching Non-Classical Logic in the past years, and the response from my students shows the great success of the author's intention. The proof system it employs and the meta-proofs it provides are extremely easy to follow, while those followed-up philosophical discussions it summarizes for each logic system are both concise and lucid. It is not only a work introducing modern non-classical logic systems, but also a work full of interesting philosophical discussions on the motivations, advantages and disadvantages of these systems. With one penetrating theme - what a logic of conditionals should be like - in mind, the author has effectively organized a variety of topics into one integrated work. I would recommend it both to logicians and to philosophers, to professionals and to non-professionals.' Wen-fang Wang, National Chung Chen University'The second edition of Graham Priest's book is, like the first, clearly expressed, well thought out for the student and an essential work for all those studying philosophy who want an adequate grounding in non-classical logic. I have used the first edition successfully in my intermediate class for the last five years, and will certainly be adding the second edition to the reading list when it is available.' Steve Read, University of St Andrews'Priest succeeds in offering a marvellously unified treatment of 11 varieties of logic: classical, basic modal, normal modal, non-normal, conditional, intuitionist, many-valued, first-degree entailment, basic relevant, mainstream relevant, and fussy … Excellent references support this concise but clear treatment.' Choice'This book is just what the title says it is … And it is a very good one …' Stewart Shapiro, University of Ohio' … for anyone who wants to explore the non-classical systems, it is the only book of its kind and could not be more highly recommended.' The Times Higher Education Supplement'I've just picked up a copy of the second edition of Graham Preist's An Introduction to Non-Classical Logic from the CUP bookshop. It looks terrific. More than twice the length of the first edition which just covered propositional logics, this covers their extensions with quantifiers and identity too. I thought the fist edition was terrific: so this is a hugely welcome expansion and I'm delighted to report that CUP has published this as a paperback in their Cambridge Introductions to Philosophy Series at just £18.99, which is surely an amazing bargain for a well produced 613 page book. So a must-buy and a must-read!' Logic MattersTable of ContentsPreface to the first edition; Preface to the second edition; Mathematical prolegomenon; Part I. Propositional Logic: 1. Classical logic and the material conditional; 2. Basic modal logic; 3. Normal modal logics; 4. Non-normal modal logics; strict conditionals; 5. Conditional logics; 6. Intuitionist logic; 7. Many-valued logics; 8. First degree entailment; 9. Logics with gaps, gluts, and worlds; 10. Relevant logics; 11. Fuzzy logics; 11a. Appendix: many valued modal logics; Postscript: an historical perspective on conditionals; Part II. Qualification and Identity: 12. Classical logic; 13. Free logic; 14. Constant domain modal logics; 15. Variable domain modal logics; 16. Necessary identity in modal logic; 17. Contingent identity in modal logic; 18. Non-normal modal logics; 19. Conditional logics; 20. Intuitionist logic; 21. Many-valued logics; 22. First degree entailment; 23. Logics with gaps, gluts, and worlds; 24. Relevant logics; 25. Fuzzy logics; Postscript: a methodological coda.
£89.99
Cambridge University Press An Introduction to ManyValued and Fuzzy Logic Semantics Algebras and Derivation Systems
Book SynopsisProfessor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic - problems arising from vague language - and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems - Lukasiewicz, GÃdel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.Trade Review"Bergmann has done an excellent job...Highly recommended." R. Bharath, Northern Michigan University, ChoiceTable of ContentsPreface; 1. Introduction; 2. Review of classical propositional logic; 3. Review of classical first-order logic; 4. Alternative semantics for truth-values and truth-functions; 5. Three-valued propositional logics: semantics; 6. Derivation systems for three-valued propositional logic; 7. Three-valued first-order logics: semantics; 8. Derivation systems for three-valued first-order logics; 9. Alternative semantics for three-valued systems; 10. The principle of charity reconsidered and a new problem of the fringe; 11. Fuzzy propositional logics: semantics; 12. Fuzzy algebras; 13. Derivational systems for fuzzy propositional logics; 14. Fuzzy first-order logics: semantics; 15. Derivation systems for fuzzy first-order logics; 16. Extensions of fuzziness; 17. Fuzzy membership functions.
£89.99
Cambridge University Press Logic Colloquium 2005
Book SynopsisHighlights of this 2007 volume from the Annual European Meeting of the ASL include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.Table of Contents1. Thread algebra and risk assessment services Jan A. Bergstra, Inge Bethke and Alban Ponse; 2. Covering definable manifolds by open definable subsets Mário J. Edmundo; 3. Isomorphisms and definable relations on computable models Sergei S. Goncharov; 4. Independence for types in algebraically closed valued fields Deirdre Haskell; 5. Simple groups of finite Morley rank Eric Jaligot; 6. Towards a logic of type-free modality and truth Hannes Leitgeb; 7. Structural analysis of Aronszajn trees Justin Tatch Moore; 8. Proof analysis in non-classical logics Sara Negri; 9. Paul Bernays' later philosophy of mathematics Charles Parsons; 10. Proofnets for S5: sequents and circuits for modal logic Greg Restall; 11. Recursion on the partial continuous functionals Helmut Schwichtenberg; 12. A transactional approach to the logic of truth Michael Sheard; 13. On some problems in computable topology Dieter Spreen; 14. Monotone inductive definitions and consistency of New Foundations Sergei Tupailo.
£105.45
Cambridge University Press Subsystems of Second Order Arithmetic
Book SynopsisWhat are the appropriate axioms for mathematics? Through a series of case studies, this volume examines these axioms to prove particular theorems in core areas including algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics.Table of ContentsList of tables; Preface; Acknowledgements; 1. Introduction; Part I. Development of Mathematics within Subsystems of Z2: 2. Recursive comprehension; 3. Arithmetical comprehension; 4. Weak König's lemma; 5. Arithmetical transfinite recursion; 6. π11 comprehension; Part II. Models of Subsystems of Z2: 7. β-models; 8. ω-models; 9. Non-ω-models; Part III. Appendix: 10. Additional results; Bibliography; Index.
£141.00
Cambridge University Press Graph Structure and Monadic SecondOrder Logic A LanguageTheoretic Approach 138 Encyclopedia of Mathematics and its Applications Series Number 138
Book SynopsisThe study of graph structure has advanced with great strides. This book unifies and synthesizes research over the last 25 years, detailing both theory and application. It will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.Trade Review'In its huge breadth and depth the authors manage to provide a comprehensive study of monadic second-order logic on graphs covering almost all aspects of the theory that can be presented from a language theoretical or algebraic point of view. There is currently no other textbook or any other source that matches the range of materials covered in this book. As such it is a fantastic resource for those who to study this area [and] will undoubtedly turn into the standard reference for this area.' Stephan Kreutzer, Mathematical ReviewsTable of ContentsForeword Maurice Nivat; Introduction; 1. Overview; 2. Graph algebras and widths of graphs; 3. Equational and recognizable sets in many-sorted algebras; 4. Equational and recognizable sets of graphs; 5. Monadic second-order logic; 6. Algorithmic applications; 7. Monadic second-order transductions; 8. Transductions of terms and words; 9. Relational structures; Conclusion and open problems; References; Index of notation; Index.
£169.00
Cambridge University Press LambdaCalculus and Combinators An Introduction
Book SynopsisCombinatory logic and lambda-calculus, originally devised in the 1920s, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this version is thoroughly revised and offers an account of the subject with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.Trade ReviewFrom reviews of the first edition: 'The book of R. Hindley and J. Seldin is a very good introduction to fundamental techniques and results in these fields ... the book is clear, pleasant to read, and it needs no previous knowledge in the domain, but only basic notions of mathematical logic ... Clearly, it was impossible to treat everything in detail; but even when a subject is only skimmed, the book always provides an incentive for going deeper, and furnishes the means to do it, owing to a substantial bibliography. Several chapters end with interesting and useful notes with history, comments, and indications for further reading ... In conclusion, this book is very interesting and well written, and is highly recommended to everyone who wants to approach combinatory logic and lambda-calculus (logicians or computer scientists). J. Symbolic Logic'The best general book on lambda-calculus (typed or untyped) and the theory of combinators.' Gérard Huet, INRIA'… for teaching and for research or self-study the book is an outstanding source with its own clear merits. I think this second edition of this classical book is a beautiful asset for the literature on λ-calculus and CL.' Theory and Practice of Logic Programming'… well written and offers a broad coverage backed by an extensive list of references. It could serve as an excellent study material for classes on λ-calculus and CL as well as a reference for logicians and computer scientists interested in the formal background for functional programming and related areas.' EMS Newsletter'Without doubt this is a valuable treatment of a venerable topic that rewards those who understand it. The authors successfully promulgate their tradition, and that is certainly more important than providing full proofs for every result.' The Journal of JFPTable of ContentsPreface; 1. The λ-calculus; 2. Combinatory logic; 3. The power of λ and CL; 4. Computable functions; 5. Undecidability; 6. Formal theories; 7. Extensionality in λ-calculus; 8. Extensionality in CL; 9. Correspondence between λ and CL; 10. Simple typing, Church-style; 11. Simple typing, Curry-style in CL; 12. Simple typing, Curry-style in λ; 13. Generalizations of typing; 14. Models of CL; 15. Models of λ ; 16. Scott's D∞ and other models; Appendix 1. α-conversion; Appendix 2. Confluence proofs; Appendix 3. Normalization proofs; Appendix 4. Care of your pet combinator; Appendix 5. Answers to starred exercises; Bibliography; Index.
£64.99
Springer Newtons Method and Dynamical Systems Spinoff Acta Applicandae Mathematical Vol 13 12
Book SynopsisNewton's Method and Complex Dynamical Systems.- Discrete Versus Continuous Newton's Method: A Case Study.- The Continuous, Desingularized Newton Method for Meromorphic Functions.- Global Aspects of the Continuous and Discrete Newton Method: A Case Study.- Idiosyncratic Remarks by a Bibliomaniac: 5. A Random Sample of Structured Chaos.- Book Review: An introduction to Chaotic Dynamical Systems (Floris Takens).Table of ContentsNewton’s Method and Complex Dynamical Systems.- Discrete Versus Continuous Newton’s Method: A Case Study.- The Continuous, Desingularized Newton Method for Meromorphic Functions.- Global Aspects of the Continuous and Discrete Newton Method: A Case Study.- Idiosyncratic Remarks by a Bibliomaniac: 5. A Random Sample of Structured Chaos.- Book Review: An introduction to Chaotic Dynamical Systems (Floris Takens).
£999.99
Springer Mathematical Intuition
Book Synopsis"Intuition" has perhaps been the least understood and the most abused term in philosophy. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge.Trade Review`This book is a very welcome addition to the small number of texts which succeed in bridging the gap between the phenomenological tradition in philosophy of mathematics and the analytic tradition. The author shows very convincingly that the phenomenological tradition is a rich source of subtle and fertile ideas which are highly relevant to central problems in contemporary philosophy of mathematics.' Mathematical ReviewsTable of Contents1. The Concept of Intuition in Mathematics.- 1. Introduction.- 2. Knowledge, Evidence, and Intuition.- 3. Intuition “of” and Intuition “that”.- 4. Some Recent Views of Mathematical Intuition.- 5. Hilbert and Bernays.- 6. Parsons.- 7. Brouwer.- 8. Some “Extended” Proof-Theoretic Views.- 9. Gödel on Sets.- 10. Platonism and Constructivism.- 11. Mathematical Truth and Mathematical Knowledge.- 12. Principal Objections to Mathematical Intuition.- 2. The Phenomenological View of Intuition.- 1. Introduction.- 2. Intentionality and Intuition.- 3. Intuition of Abstract Objects.- 4. Acts of Abstraction and Abstract Objects.- 5. Acts of Reflection.- 6. Types and Degrees of Evidence.- 7. Comparison with Kant.- 8. Intuition and the Theory of Meaning.- 3. Perception.- 1. Introduction.- 2. Sequences of Perceptual Acts.- 3. The Horizon of Perceptual Acts.- 4. The Possibilities of Perception.- 5. The “Determinable X” in Perception and Indexicals.- 6. Perceptual Evidence.- 7. Phenomenological Reduction and the Problem of Realism / Idealism.- 4. Mathematical Intuition.- 1. Introduction.- 2. Objections About Analogies Between Perceptual and Mathematical Intuition.- 3. Objections Based on Structuralism.- 4. Objections About Founding.- 5. A Logic Compatible With Mathematical Intuition and the Notion of Construction.- 6. Is Classical Mathematics to be Rejected?.- 5. Natural Numbers I.- 1. Introduction.- 2. The Concept of Number Cannot Be Explicitly Defined.- 3. The Origin of the Concept of Number.- 4. Intuition of Natural Numbers.- 5. Ordinals.- 6. Ordinals and Cardinals.- 7. Constructing Units and the Role of Reflection and Abstraction.- 8. Syntax and Representations of Numbers.- 6. Natural Numbers II.- 1. Introduction.- 2. 0 and 1.- 3. Numbers Formed by Arithmetic Operations.- 4. Small Numbers and Singular Statements About Them.- 5. Large Numbers and Mathematical Induction.- 6. The Possibilities of Intuition.- 7. Summary of the Argument for Large Numbers.- 8. Further Comments on Mathematical Induction.- 9. Intuition and Axioms of Elementary Number Theory.- 7. Finite sets.- 1. Introduction.- 2. A Theory of Finite Sets.- 3. The Origin of the Concept of Finite Set.- 4. Intuition of Finite Sets.- 5. Comparison with Gödel and Wang.- 6. Unit Sets, the Empty Set, and Mereology vs. Set Theory.- 7. Large Sets and a Hierarchy of Sets.- 8. Illusion in Set Theory.- 9. Concluding Remarks.- 8. Critical Reflections and Conclusion.- 1. Introduction.- 2. Summary of the Account.- 3. Areas for Further Work.- 4. Platonism, Constructivism, and Benacerraf’s Dilemma.- Notes.
£999.99
Springer Acting and Reflecting The Interdisciplinary Turn in Philosophy 211 Synthese Library
Book SynopsisI. Philosophy?.- 1. Philosophy and the Sciences.- 2. Impressions of Philosophy.- 3. The Computational Model of the Mind, a panel discussion.- 4. Discussion: Progress in Philosophy.- 5. Philosophy and the Academy.- II. Working..- 1. Pale Fire Solved.- 2. Incremental Acquisition and a Parametrized Model of Grammar.- 3. What are General Equilibrium Theories?.- 4. Effective Epistemology, Psychology, and Artificial Intelligence.- 5. The Flaws in Sen's Case Against Paretian Libertariansism.- 6. Decisions without Ordering.- 7. Reflections on Hilbert's Program.- 8. The Tetrad Project.- III. Postscriptum.- 1. Rationality Unbound.Table of ContentsI. Philosophy?.- 1. Philosophy and the Sciences.- 2. Impressions of Philosophy.- 3. The Computational Model of the Mind, a panel discussion.- 4. Discussion: Progress in Philosophy.- 5. Philosophy and the Academy.- II. Working..- 1. Pale Fire Solved.- 2. Incremental Acquisition and a Parametrized Model of Grammar.- 3. What are General Equilibrium Theories?.- 4. Effective Epistemology, Psychology, and Artificial Intelligence.- 5. The Flaws in Sen’s Case Against Paretian Libertariansism.- 6. Decisions without Ordering.- 7. Reflections on Hilbert’s Program.- 8. The Tetrad Project.- III. Postscriptum.- 1. Rationality Unbound.
£999.99
