Computability and Logic
by George S. Boolos , John P. Burgess , Richard C. JeffreyEdition: 5th
Format: Paperback
Pub. Date: 2007-09-17
Publisher(s): Cambridge University Press
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Summary
Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This new edition is also accompanied by a website as well as an instructor's manual.
Table of Contents
| Computability Theory | |
| Enumerability | |
| Diagonalization | |
| Turing computability | |
| Uncomputability | |
| Abacus computability | |
| Recursive functions | |
| Recursive sets and relations | |
| Equivalent definitions of computability | |
| Basic Metalogic | |
| A precis of first-order logic: syntax | |
| A precis of first-order logic: semantics | |
| The undecidability of first-order logic | |
| Models | |
| The existence of models | |
| Proofs and completeness | |
| Arithmetization | |
| Representability of recursive functions | |
| Indefinability, undecidability, incompleteness | |
| The unprovability of consistency | |
| Further Topics | |
| Normal forms | |
| The Craig interpolation theorem | |
| Monadic and dyadic logic | |
| Second-order logic | |
| Arithmetical definability | |
| Decidability of arithmetic without multiplication | |
| Non-standard models | |
| Ramsey's theorem | |
| Modal logic and provability | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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