Mathematical logic Books
World Scientific Publishing Co Pte Ltd E-recursion, Forcing And C*-algebras
Book SynopsisThis volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School. The major topics cover set-theoretic forcing, higher recursion theory, and applications of set theory to C*-algebra. This volume offers a wide spectrum of ideas and techniques introduced in contemporary research in the field of mathematical logic to students, researchers and mathematicians.
£66.50
World Scientific Publishing Co Pte Ltd E-recursion, Forcing And C*-algebras
Book SynopsisThis volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School. The major topics cover set-theoretic forcing, higher recursion theory, and applications of set theory to C*-algebra. This volume offers a wide spectrum of ideas and techniques introduced in contemporary research in the field of mathematical logic to students, researchers and mathematicians.
£21.85
World Scientific Publishing Co Pte Ltd Magic Garden Of George B And Other Logic Puzzles,
Book SynopsisRaymond Smullyan presents a bombshell puzzle so startling that it seems incredible that there could be any solution at all! But there is indeed a solution — moreover, one that requires a chain of lesser puzzles to be solved first. The reader is thus taken on a journey through a maze of subsidiary problems that has all the earmarks of an entertaining detective story.This book leads the unwary reader into deep logical waters through seductively entertaining logic puzzles. One example is Boolean algebra with such weird looking equations as 1+1=0 — a subject which today plays a vital role, not only in mathematical systems, but also in computer science and artificial intelligence.Table of ContentsIt's All A Question of Logic: Puzzles or Monkey Tricks; Which Lady; Which Witch; Which Island; McGregor's Arithmetic Tricks; Ask Eldon White; Al, the Chemist; Sane or Mad; The Strange Case of McSnurd; The Knight-Knave Disease; Human or Android; Variable Lying and Paradox; The Magic Garden: George's Garden; Some Neighboring Gardens; The Grand Problem Solved!; Boolean Gardens and Variable Liars; Propositional Logic and Boolean Gardens; The Boolean Theory of Sets; Boolean Algebras in General; Boolean Gardens Revisited; Another Grand Problem; George Boole and Mathematical Logic;
£45.60
World Scientific Publishing Co Pte Ltd Proceedings Of The 13th Asian Logic Conference
Book SynopsisThis volume provides a forum which highlights new achievements and overviews of recent developments of the thriving logic groups in the Asia-Pacific region. It contains papers by leading logicians and also some contributions in computer science logics and philosophic logics.Table of ContentsAn Analogy Between Cardinal Characteristics and Highness Properties of Oracles (Jorg Brendle, Andrew Brooke-Taylor, Keng Meng Ng and Andre Nies); Minimal Pairs in the C. E. Truth-Table Degrees (Rod Downey, Keng Meng Ng); Degree Spectra of Equivalence Relations (Liang Yu); Some Questions Concerning Ab Initio Generic Structures (Koichiro Ikeda); Model Complete Generic Structures (Koichiro Ikeda and Hirotaka Kikyo); Large Cardinals and Higher Degree Theory (Xianghui Shi); Characterization of the Second Homology Group of a Stationary Type in a Stable Theory (John Goodrick, Byunghan Kim and Alexei Kolesnikov); On Categorical Relationship Among Various Fuzzy Topological Systems, Fuzzy Topological Spaces and Related Algebraic Structures (Purbita Jana and Mihir K Chakraborty); Realizability and Existence Property of a Constructive Set Theory with Types (F Kachapova); A Non-Uniformly C-Productive Sequence & Non-Constructive Disjunctions (John Case, Michael Ralston and Yohji Akama); On Extensions of Basic Propositional Logic (Minghui Ma and Katsuhiko Sano); Goal-Directed Unbounded Coalitional Game and Its Complexity (Hu Liu); A Survey on Recent Results on Partial Learning (Ziyuan Gao, Sanjay Jain, Frank Stephan and Sandra Zilles);
£94.05
World Scientific Publishing Co Pte Ltd Magic Garden Of George B And Other Logic Puzzles,
Book SynopsisRaymond Smullyan presents a bombshell puzzle so startling that it seems incredible that there could be any solution at all! But there is indeed a solution — moreover, one that requires a chain of lesser puzzles to be solved first. The reader is thus taken on a journey through a maze of subsidiary problems that has all the earmarks of an entertaining detective story.This book leads the unwary reader into deep logical waters through seductively entertaining logic puzzles. One example is Boolean algebra with such weird looking equations as 1+1=0 — a subject which today plays a vital role, not only in mathematical systems, but also in computer science and artificial intelligence.Table of ContentsIt's All A Question of Logic: Puzzles or Monkey Tricks; Which Lady; Which Witch; Which Island; McGregor's Arithmetic Tricks; Ask Eldon White; Al, the Chemist; Sane or Mad; The Strange Case of McSnurd; The Knight-Knave Disease; Human or Android; Variable Lying and Paradox; The Magic Garden: George's Garden; Some Neighboring Gardens; The Grand Problem Solved!; Boolean Gardens and Variable Liars; Propositional Logic and Boolean Gardens; The Boolean Theory of Sets; Boolean Algebras in General; Boolean Gardens Revisited; Another Grand Problem; George Boole and Mathematical Logic;
£22.80
World Scientific Publishing Co Pte Ltd Forcing, Iterated Ultrapowers, And Turing Degrees
Book SynopsisThis volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2010 and 2011 Asian Initiative for Infinity Logic Summer Schools. The major topics covered set theory and recursion theory, with particular emphasis on forcing, inner model theory and Turing degrees, offering a wide overview of ideas and techniques introduced in contemporary research in the field of mathematical logic.
£71.25
World Scientific Publishing Co Pte Ltd Introduction To Mathematical Logic (Extended
Book SynopsisThis is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students.Starting with the basics of set theory, induction and computability, it covers propositional and first order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts.Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic.This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. An equivalence of logical and graphical representations allows us to see vicious circularity as the odd cycles in the graphical representation and can be used as a simple tool for diagnosing paradoxes in natural discourse.Table of ContentsA History of Logic: Patterns of Reasoning; A Language and Its Meaning; A Symbolic Language; 1850-1950 - Mathematical Logic; Modern Symbolic Logic; Summary; Elements of Set Theory: Sets, Functions, Relations; Induction; Turing Machines: Computability and Decidability; Propositional Logic: Syntax and Proof Systems; Semantics of PL; Soundness and Completeness; Diagnosing Paradoxes; First Order Logic: Syntax and Proof Systems of FOL; Semantics of FOL; More Semantics; Soundness and Completeness; Why is First Order Logic "First Order"?;
£38.00
World Scientific Publishing Co Pte Ltd Introduction To Mathematical Logic (Extended
Book SynopsisThis is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students.Starting with the basics of set theory, induction and computability, it covers propositional and first order logic — their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts.Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules — of a high, though often neglected, pedagogical value — aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic.This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. An equivalence of logical and graphical representations allows us to see vicious circularity as the odd cycles in the graphical representation and can be used as a simple tool for diagnosing paradoxes in natural discourse.Table of ContentsA History of Logic: Patterns of Reasoning; A Language and Its Meaning; A Symbolic Language; 1850-1950 - Mathematical Logic; Modern Symbolic Logic; Summary; Elements of Set Theory: Sets, Functions, Relations; Induction; Turing Machines: Computability and Decidability; Propositional Logic: Syntax and Proof Systems; Semantics of PL; Soundness and Completeness; Diagnosing Paradoxes; First Order Logic: Syntax and Proof Systems of FOL; Semantics of FOL; More Semantics; Soundness and Completeness; Why is First Order Logic "First Order"?;
£67.45
World Scientific Publishing Co Pte Ltd Beginner's Further Guide To Mathematical Logic, A
Book Synopsis'A wealth of examples to which solutions are given permeate the text so the reader will certainly be active.'The Mathematical GazetteThis is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a 'fein' chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a 'decision machine.' Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.
£19.00
World Scientific Publishing Co Pte Ltd Beginner's Further Guide To Mathematical Logic, A
Book Synopsis'A wealth of examples to which solutions are given permeate the text so the reader will certainly be active.'The Mathematical GazetteThis is the final book written by the late great puzzle master and logician, Dr. Raymond Smullyan.This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and first-order logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and first-order logic, followed by what I would call a 'fein' chapter, which simultaneously generalizes some results from recursion theory, first-order arithmetic systems, and what I dub a 'decision machine.' Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.
£53.20
Springer Mathematical Logic for Computer Science
Book SynopsisPreface.- Introduction.- Propositional Logic: Formulas, Models, Tableaux.- Propositional Logic: Deductive Systems.- Propositional Logic: Resolution.- Propositional Logic: Binary Decision Diagrams.- Propositional Logic: SAT Solvers.- First-Order Logic: Formulas, Models, Tableaux.- First-Order Logic: Deductive Systems.- First-Order Logic: Terms and Normal Forms.- First-Order Logic: Resolution.- First-Order Logic: Logic Programming.- First-Order Logic: Undecidability and Model Theory.- Temporal Logic: Formulas, Models, Tableaux.- Temporal Logic: A Deductive System.- Verification of Sequential Programs.- Verification of Concurrent Programs.- Set Theory.- Index of Symbols.- Index of Names.- Subject Index.Trade ReviewAsst. Prof. Manoj Raut, Dhirubhai Ambani Institute of Information and Communication Technology, IndiaExcerpts from full review posted Jan 15 2013 to Computing Reviews [Review #: CR140831]I have used the second edition of this book for my class. I find this new third edition more interesting and more elaborately written; I like it very much, and applaud the author for his work.Table of ContentsPreface.- Introduction.- Propositional Logic: Formulas, Models, Tableaux.- Propositional Logic: Deductive Systems.- Propositional Logic: Resolution.- Propositional Logic: Binary Decision Diagrams.- Propositional Logic: SAT Solvers.- First-Order Logic: Formulas, Models, Tableaux.- First-Order Logic: Deductive Systems.- First-Order Logic: Terms and Normal Forms.- First-Order Logic: Resolution.- First-Order Logic: Logic Programming.- First-Order Logic: Undecidability and Model Theory.- Temporal Logic: Formulas, Models, Tableaux.- Temporal Logic: A Deductive System.- Verification of Sequential Programs.- Verification of Concurrent Programs.- Set Theory.- Index of Symbols.- Index of Names.- Subject Index.
£52.24
Springer Fachmedien Wiesbaden Mengenlehre und ihre Logik
Book SynopsisEinführung.- Erster Teil: Die Elemente.- I. Logik.- II. Reale Klassen.- III. Klassen von Klassen.- IV. Natürliche Zahlen.- V. Iteration und Arithmetik.- Zweiter Teil: Höhere Zahlformen.- VI. Reelle Zahlen.- VII. Ordnung und Ordinalzahlen.- VIII. Transfinite Rekursion.- IX. Kardinalzahlen.- X. Das Auswahlaxiom.- Dritter Teil: Axiomensysteme.- XI. Die Russellsche Typentheorie.- XII. Universelle Variablen und Zermelo.- XIII. Stratifizierung und äußerste Klassen.- XIV. Das System von von Neumann und andere Systeme.- Vierter Teil: Anhang.- I. Zusammenstellung von fünf Axiomensystemen.- II. Liste durchnumerierter Formeln.- III. Bibliographie.- Sachwortverzeichnis.Table of ContentsEinführung.- Erster Teil: Die Elemente.- I. Logik.- 1. Quantifizierung und Identität.- 2. Virtuelle Klassen.- 3. Virtuelle Relationen.- II. Reale Klassen.- 4. Realität, Extensionalität und Individuen.- 5. Das Virtuelle unter dem Realen.- 6. Identität und Einsetzung.- III. Klassen von Klassen.- 7. Einerklassen.- 8. Vereinigungen, Durchschnitte, Kennzeichnungen.- 9. Relationen als Klassen von Klassen.- 10. Funktionen.- IV. Natürliche Zahlen.- 11. Zahlen — naiv.- 12. Zahlen — konstituiert.- 13. Induktion.- V. Iteration und Arithmetik.- 14. Folgen und Iterierte.- 15. Die Vorfahrenrelation.- 16. Summe, Produkt, Potenz.- Zweiter Teil: Höhere Zahlformen.- VI. Reelle Zahlen.- 17. Programm; Zahlenpaare.- 18. Rationale und reelle Zahlen — konstituiert.- 19. Existenzforderungen. Operationen und Erweiterungen.- VII. Ordnung und Ordinalzahlen.- 20. Transfinite Induktion.- 21. Ordnung.- 22. Ordinalzahlen.- 23. Sätze über Ordinalzahlen.- 24. Die Ordnung der Ordinalzahlen.- VIII. Transfinite Rekursion.- 25. Transfinite Rekursion.- 26. Sätze über transfinite Rekursion.- 27. Aufzählung.- IX. Kardinalzahlen.- 28. Relative Größe von Klassen.- 29. Das Schröder-Bernsteinsche Theorem.- 30. Unendliche Kardinalzahlen.- X. Das Auswahlaxiom.- 31. Selektionen und Selektoren.- 32. Weitere äquivalente Formulierungen des Axioms.- 33. Die Stellung des Axioms.- Dritter Teil: Axiomensysteme.- XI. Die Russellsche Typentheorie.- 34. Der konstruktive Teil.- 35. Klassen und das Reduzibilitätsaxiom.- 36. Die moderne Typentheorie.- XII. Universelle Variablen und Zermelo.- 37. Die Typentheorie mit universellen Variablen.- 38. Kumulative Typen und Zermelo.- 39. Unendlichkeitsaxiome und andere.- XIII. Stratifizierung und äußerste Klassen.- 40. New foundations.- 41. Nicht-Cantorsche Klassen. Noch einmal Induktion.- 42. Hinzufügen äußerster Klassen.- XIV. Das System von von Neumann und andere Systeme.- 43. Das System von von Neumann-Bernays.- 44. Abweichungen und Vergleiche.- 45. Die Stärke der verschiedenen Systeme.- Vierter Teil: Anhang.- I. Zusammenstellung von fünf Axiomensystemen.- II. Liste durchnumerierter Formeln.- III. Bibliographie.- Sachwortverzeichnis.
£999.99
Springer Fachmedien Wiesbaden Diskrete Mathematik mit Grundlagen: Lehrbuch für
Book SynopsisDieses Lehrbuch wendet sich an Leser ohne Studienvorkenntnisse, gibt eine elementare Einführung in die Diskrete Mathematik und die Welt des mathematischen Denkens und führt den Leser auf ein solides Hochschulniveau. Im Einzelnen werden elementare Logik, Mengenlehre, Beweiskonzepte und die mathematische Terminologie dafür ausführlich erklärt und durch Anwendungsbeispiele motiviert. Darauf aufbauend werden die wichtigsten Disziplinen der Diskreten Mathematik behandelt in einem Umfang, der für jedes MINT-Studium außer der Mathematik selbst ausreicht. Zahlreiche Übungsaufgaben runden das Angebot ab, die Lösungen dazu werden online zur Verfügung gestellt. Das Buch ist zum Selbststudium, als Vorlesungsbegleitung und zum Nachschlagen geeignet. Die zweite Auflage wurde vollständig überarbeitet. Das Kapitel zur Logik wurde erheblich ausgeweitet, unter anderem durch eine allgemeinverständliche Anleitung mit vielen Beispielen, wie Alltagssprache in logische Sprache übersetzt wird.Table of ContentsLogik.- Mengenlehre.- Beweisverfahren.- Zahlentheorie.- Algebraische Strukturen.- Kombinatorik.- Graphentheorie.
£27.99
World Scientific Publishing Co Pte Ltd Communicating The Quantum Way
Book Synopsis
£114.00
Springer Nature Switzerland AG New Foundations for Information Theory: Logical Entropy and Shannon Entropy
Book SynopsisThis monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications.Information is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or “dit” of the partition will be obtained. The formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory) and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits—so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general—and to Hilbert spaces in particular—for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement.Relatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory, maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to quantum information theory.Table of Contents- Logical entropy.- The relationship between logical entropy and Shannon entropy.- The compound notions for logical and Shannon entropies.- Further developments of logical entropy.- Logical Quantum Information Theory.- Conclusion.- Appendix: Introduction to the logic of partitions.
£49.49
Springer International Publishing AG Sets, Models and Proofs
Book SynopsisThis textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas.The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.Trade Review“This text is very well written and does an excellent job introducing the subject matter to a student. Even if your school does not have a course covering these topics, I would recommend the text for a student conducting an independent study of the material.” (Geoffrey D. Dietz, MAA Reviews, July 28, 2019)“This book is one of a few excellent textbooks for a one-semester introductory mathematical logic course for undergraduate students with relevant majors. It achieves a good balance between depth and brevity. It fits the needs of a student who wants to explore the subject but does not want to be bogged down by excessive demands of rigor before appreciation for mathematical logic can be developed. ... This book is short but self-contained and … interesting exercises complement the main theorems.” (Renling Jin, Mathematical Reviews, September, 2019)Table of ContentsIntroduction.- 1 Sets.- 2 Models.- 3 Proofs.- 4 Sets Again.- Appendix: Topics for Further Study.- Photo Credits.- Bibliography.- Index.
£26.59
AV Akademikerverlag Drayage Operations at Seaports
£34.57
Kings College Publications The Haskell Road to Logic Maths and Programming
£17.50
Advanced Reasoning Forum Computability Computable Functions Logic and the Foundations of Mathematics
£39.57
Advanced Reasoning Forum Propositional Logics Third Edition
£39.57
Cambridge University Press Formal Languages in Logic A Philosophical And Cognitive Analysis
Book SynopsisFormal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science.Trade Review'Since the rise of logical empiricism, formal languages have become essential tools of doing philosophy. But why does formalization work? And what are its limitations? This book fills a crucial gap in the literature by addressing these questions from a cognitive, historical, and logical point of view. I recommend it to formal philosophers, critics of formal philosophy, and everyone with an interest in the techniques of conceptual engineering per se.' Hannes Leitgeb, Ludwig Maximilians Universität MunichTable of ContentsIntroduction; 1. Two notions of formality; 2. On the very notion of a formal language; 3. The history, purposes and limitations of formal languages; 4. How we do reason, and the need for counterbalance in science; 5. Formal languages and extended cognition; 6. De-semantification; 7. The debiasing effect of formalization; Conclusion.
£37.37
Digireads.com The Cloud of Unknowing
£9.31
Springer Introduction to Mathematical Structures and Proofs
Book SynopsisPreface to the Second Edition.- Preface to the First Edition.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets.- 5. Combinatorics.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index.Table of Contents-Preface.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets. - 5. Permutations and Combinations.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index
£40.99
Birkhauser Boston Theory of Finite and Infinite Graphs
Book SynopsisCommentary.- Theory of Finite and Infinite Graphs.- Dénes König: A Biographical Sketch.Table of ContentsCommentary.- Theory of Finite and Infinite Graphs.- Dénes König: A Biographical Sketch.
£42.74
Cosimo Classics An Investigation of the Laws of Thought
£16.54
College Publications Studies in Diagrammatology and Diagram Praxis
£18.50
College Publications Passed Over in Silence. On Wittgenstein's Tractatus and Its System
£19.95
College Publications Hao Wang. Logician and Philosopher
£14.00
College Publications Inconsistent Geometry
£25.65
College Publications Foundations of Mathematics I
£18.00
College Publications Handbook of Mathematical Fuzzy Logic. Volume 1
£20.00
College Publications Set Theory
Book SynopsisThis book is designed for readers who knowelementary mathematical logic and axiomatic settheory, and who want to learn more about set theory.The primary focus of the book is on the independenceproofs. Most famous among these is the independenceof the Continuum Hypothesis (CH); that is, there aremodels of the axioms of set theory (ZFC) in whichCH is true, and other models in which CH is false.More generally, cardinal exponentiation on the regularcardinals can consistently be anything not contradictingthe classical theorems of Cantor and König.The basic methods for the independence proofs arethe notion of constructibility, introduced by Gödel, andthe method of forcing, introduced by Cohen. This bookdescribes these methods in detail, verifi es the basicindependence results for cardinal exponentiation, andalso applies these methods to prove the independenceof various mathematical questions in measure theoryand general topology.Before the chapters on forcing, there is a fairly longchapter on "infi nitary combinatorics". This consistsof just mathematical theorems (not independenceresults), but it stresses the areas of mathematicswhere set-theoretic topics (such as cardinal arithmetic)are relevant.There is, in fact, an interplay between infi nitarycombinatorics and independence proofs. Infi nitarycombinatorics suggests many set-theoretic questionsthat turn out to be independent of ZFC, but it alsoprovides the basic tools used in forcing arguments. Inparticular, Martin''s Axiom, which is one of the topicsunder infi nitary combinatorics, introduces many of thebasic ingredients of forcing.
£18.00
College Publications Handbook of Mathematical Fuzzy Logic. Volume 2
£20.00
College Publications Trends in Belief Revision and Argumentation Dynamics
£15.00
College Publications Modestly Radical or Radically Modest
£13.50
College Publications Insolubles and Consequences
£15.00
College Publications The Road Not Taken. On Husserl's Philosophy of Logic and Mathematics
£17.50
College Publications Errors of Reasoning. Naturalizing the Logic of Inference
£20.00
College Publications Handbook of Deontic Logic and Normative Systems
£19.95
College Publications Questions, Inferences, and Scenarios
£13.00
College Publications Intuitionistic Set Theory
£13.70
College Publications Introduction to Propositional Satisfiability
£16.00
College Publications La Logica Como Herramienta de La Razon
£13.70
College Publications Handbook of Epistemic Logic
£22.35
College Publications Proof Theory of N4-Paraconsistent Logics
£18.02
College Publications Why is this a Proof?
£13.50
College Publications The Foundations of Mathematics
£18.50
College Publications How to Sell a Contradiction: The Logic and Metaphysics of Inconsistency
£22.32
