Computability and Logic

Computability and Logic

3.94 (96 ratings by Goodreads)
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Description

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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • Revised
  • 4th Revised edition
  • 55 b/w illus.
  • 1139164937
  • 9781139164931

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; 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

Rating details

96 ratings
3.94 out of 5 stars
5 34% (33)
4 39% (37)
3 19% (18)
2 4% (4)
1 4% (4)
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