Computability and Logic

Computability and Logic

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George S. Boolos, John P. Burgess, Richard C. Jeffrey
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
10. A precis of first-order logic
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