Computability and Logic
Computability and Logic
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 2007 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 simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.
- 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 G<:o>del. 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."
Book News, Inc.
Product details
September 2007Paperback
9780521701464
366 pages
254 × 178 × 19 mm
0.65kg
Available
Table of Contents
- Part I. Computability Theory:
- 1. Enumerability
- 2. Diagonalization
- 3. Turing computability
- 4. Uncomputability
- 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
- 12. Models
- 13. The existence of models
- 14. Proofs and completeness
- 15. Arithmetization
- 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.
