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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. 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.Read more
- Written at a level which requires the reader to have no mathematical background
- Covers staple topics for intermediate logic courses, but offers a large number of optional topics not available in competing books
- Fifth edition has been corrected and features a simpler treatment of the representability of recursive functions
Reviews & endorsements
"John P. Burgess (Princeton U.) and Richard C. Jeffrey continue here in the tradition set by the late Boolos to present the "principal fundamental theoretical results logic" that would necessarily include the work of Gdel. For this edition they have revised and simplified their presentation of the representability of recursive functions, rewritten a section on Robinson arithmetic, and reworked exercises. They continue to present material in a two-semester format, the first on computability theory (enumerability, diagonalization, Turing compatibility, uncomputability, abacus computability, recursive functions, recursive sets and relations, equivalent definitions of computability) and basic metalogic (syntax, semantics, the undecidability of first-order logic, models and their existence, proofs and completeness, arithmetization, representability of recursive functions, indefinability, undecidability, incompleteness and the unprobability of inconsistency). They include a slate of nine further topics, including normal forms, second-order logic and Ramsey's theorem."
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- Edition: 5th Edition
- Date Published: September 2007
- format: Paperback
- isbn: 9780521701464
- length: 366 pages
- dimensions: 254 x 178 x 19 mm
- weight: 0.65kg
- availability: Available
Table of Contents
Part I. Computability Theory:
3. Turing computability
5. Abacus computability
6. Recursive functions
7. Recursive sets and relations
8. Equivalent definitions of computability
Part II. Basic Metalogic:
9. A precis of first-order logic: syntax
10. A precis of first-order logic: semantics
11. The undecidability of first-order logic
13. The existence of models
14. Proofs and completeness
16. Representability of recursive functions
17. Indefinability, undecidability, incompleteness
18. The unprovability of consistency
Part III. Further Topics:
19. Normal forms
20. The Craig interpolation theorem
21. Monadic and dyadic logic
22. Second-order logic
23. Arithmetical definability
24. Decidability of arithmetic without multiplication
25. Non-standard models
26. Ramsey's theorem
27. Modal logic and provability.
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