Computability and Logic

Computability and Logic is a classic because of its accessibility to students without a mathematical background.

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: 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.

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, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This fifth edition was first published in 2007.