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Zusatztext "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! 2005h Informationen zum Autor Cooper, S. Barry; Cooper, S. Barry Klappentext 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, this is a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results that also serves as a guide to the direction of current research in the field. Computability Theory includes both the standard material for a first course in computability and more advanced looks at Turing degrees, forcing, Turing definability, and determinacy. The final chapter explores a variety of computability applications in mathematics and science. Zusammenfassung Offers an introduction to contemporary computability theory, techniques, and results. This book places the basic concepts and techniques of computability theory in their historical, philosophical and logical context. It includes a chapter that explores a variety of computability applications to mathematics and science. Inhaltsverzeichnis COMPUTABILITY, 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....
List of contents
COMPUTABILITY, 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.
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"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, 2005h
