Search results for "tag:"Author S. Barry Cooper""
Taylor & Francis Inc Computability Theory
Book SynopsisComputability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level.The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science.Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.Trade Review"A very nice volume indeed. Although primarily a textbook, it lives up to the author's aim to have 'plenty here to interest and inform everyone, from the beginner to the expert.' … Cooper writes in an informal style, emphasizing the ideas underlying the techniques. All the standard topics and classic results are here. … Students will find useful pointers to the literature and an abundance of exercises woven into the text." - Zentralblatt MATH, 1041 "[It] provides not only a reference repository of well-crafted proofs or proof-outlines for a large number of basic and beyond-basic facts in several areas of computability theory, but can also serve well as the textual basis for a course on the subject…"- Mathematical Reviews, 2005hTable of ContentsCOMPUTABILITY, AND UNSOLVABLE PROBLEMS: Hilbert and the Origins of Computability Theory. Models of Computability and the Church-Turing Thesis. Language, Proof and Computable Functions. Coding, Self-Reference and Diagonalisation. Enumerability and Computability. The Search for Natural Examples of Incomputable Sets. Comparing Computability. Gödel's Incompleteness Theorem. Decidable and Undecidable Theories. INCOMPUTABILITY AND INFORMATION CONTENT: Computing with Oracles. Nondeterminism, Enumerations and Polynomial Bounds. MORE ADVANCED TOPICS: Post's Problem: Immunity and Priority. The Computability of Theories. Forcing and Category. Applications of Determinacy. Computability and Structure.
£111.89
Cambridge University Press Models and Computability 259 London Mathematical Society Lecture Note Series Series Number 259
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£64.39
Cambridge University Press Sets and Proofs 258 London Mathematical Society Lecture Note Series Series Number 258
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£64.39
Imperial College Press Computability In Context: Computation And Logic
Book SynopsisComputability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way for the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier.This volume addresses various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real-world issues, covering problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world, and how this affects our way of thinking about everyday computational issues.
£121.50
Cambridge University Press Logic Colloquium 2006 32 Lecture Notes in Logic Series Number 32
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£999.99
