# Computability and Logic

Cambridge University Press

Edition: 5th edition, 11/29/2007

EAN 9780521701464, ISBN10: 0521701465

Paperback, 366 pages, 23.4 x 15.6 x 1.9 cm

Language: English

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.

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.

'... gives an excellent coverage of the fundamental theoretical results about logic involving computability, undecidability, axiomatization, definability, incompleteness, etc.' American Math Monthly