Computability theory

S. Barry Cooper

Computability theory originated with the seminal work of Godel, 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.

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[目次]

  • 3 Theory - Information Content Regained Higher Priority and Maximal Sets The Computability of Theories FORCING AND CATEGORY Forcing in Computability Theory Baire Space, Category and Measure n-Genericity and Applications Forcing with Trees, and Minimal Degrees APPLICATIONS OF DETERMINACY Gale-Stewart Games An Upper Cone of Minimal Covers Borel and Projective Determinacy, and the Global Theory of D THE COMPUTABILITY OF THEORIES Feferman's Theorem Truth versus Provability Complete extensions of Peano Arithmetic and Classes The Low Basis Theorem Arslanov's Completeness Criterion A Priority-Free Solution to Post's Problem Randomness COMPUTABILITY AND STRUCTURE Computable Models Computability and Mathematical Structures Effective Ramsey Theory Computability in Analysis Computability and Incomputability in Science FURTHER READING INDEX

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この本の情報

書名 Computability theory
著作者等 Cooper, S. B.
Cooper S. Barry
シリーズ名 Chapman & Hall/CRC mathematics
出版元 Chapman & Hall/CRC
刊行年月 c2004
ページ数 ix, 409 p.
大きさ 25 cm
ISBN 1584882379
NCID BA64717927
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言語 英語
出版国 アメリカ合衆国
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