Computability and Logic [Paperback]

Computability and Logic is a classic because of its accessibility to students without a mathematical background. This fifth edition was first published in 2007.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 Godels incompleteness theorems, but also a large number of optional topics, from Turings theory of computability to Ramseys theorem.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 Godels incompleteness theorems, but also a large number of optional topics, from Turings theory of computability to Ramseys theorem.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 Godels incompleteness theorems, but also a large number of optional topics, from Turings theory of computability to Ramseys theorem. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems.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 functil³n