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. 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.

Contents

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

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. lndefinability, Undecidability, Incompleteness

18. The Unprovability of Consistency

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. Nonstandard Models

26. Ramsey’s Theorem

27. Modal Logic and Provability

Review

“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 Godel. 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.

Book Description

Computability and Logic is a classic because of its accessibility to students without a mathematical background. This fifth edition was first published in 2007.