Computability and logic Enumerability Diagonalization Turing Computability Uncomputability Abacus Computability Recursive Functions Recursive Sets and Relations Equivalent Definitions of Computability Precis of First Order Logic: Syntax Precis of First Order Logic: Semantics Undecidability of First Order Logic Models Existence of Models Proofs and Completeness Arithmetization Representability of Recursive Functions Indefinability Undecidability Incompleteness Unprovability of Consistency Normal Forms Craig Interpolation Theorem Monadic and Dyadic Logic Second Order Logic Arithmetical Definability Decidability of Arithmetic without Multiplication Nonstandard Models Ramseys Theorem 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 such as Godels incompleteness theorems but also a large number of optional topics from Turings theory of computability to Ramseys 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 instructors manual