Computability and logic
著者
書誌事項
Computability and logic
Cambridge University Press, 2007
5th ed
- : pbk
- : hard
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注記
Includes bibliographical references (p. 341) and index
内容説明・目次
内容説明
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.
目次
- 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.
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