Computability and Logic（ISBN=9780521007580）

　　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.

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 consistencyFurther 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