Computability and logic

著者

書誌事項

Computability and logic

George S. Boolos, John P. Burgess, Richard C. Jeffrey

Cambridge University Press, 2002

4th ed

  • : pbk

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注記

Includes bibliographical references (p. 348) and index

"First published 2002. Reprinted with corrections 2003" -- T.p. verso

内容説明・目次

内容説明

This fourth edition of one of the classic logic textbooks has been thoroughly revised by John Burgess. The aim is to increase the pedagogical value of the book for the core market of students of philosophy and for students of mathematics and computer science as well. This book 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. John Burgess has now enhanced the book by adding a selection of problems at the end of each chapter, and by reorganising and rewriting chapters to make them more independent of each other and thus to increase the range of options available to instructors as to what to cover and what to defer.

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
  • 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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