Computability and Logic

Computability and Logic

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Description

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.show more

Product details

  • Paperback | 366 pages
  • 177.8 x 256.54 x 22.9mm | 566.99g
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge, United Kingdom
  • English
  • Revised
  • 5th Revised edition
  • black & white illustrations
  • 0521701465
  • 9780521701464
  • 234,460

Review quote

'... gives an excellent coverage of the fundamental theoretical results about logic involving computability, undecidability, axiomatization, definability, incompleteness, etc.' American Math Monthly 'The writing style is excellent: Although many explanations are formal, they are perfectly clear. Modern, elegant proofs help the reader understand the classic theorems and keep the book to a reasonable length.' Computing Reviews ' ... a valuable asset to those who want to enhance their knowledge and strengthen their ideas in the areas of artificial intelligence, philosophy, theory of computing, discrete structures, mathematical logic. It is also useful to teachers for improving their teaching style in these subjects.' Computer Engineeringshow more

Table of contents

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.show more