Computability and logic /
Computability & Logic
George S. Boolos, John P. Burgess , Richard C. Jeffrey.
- Fifth edition.
- Cambridge : Cambridge University Press, 2007.
- 1 online resource (xiii, 350 pages) : digital, PDF file(s).
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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 -- Ramsey's 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 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.
9780511804076 (ebook)
Computable functions. Recursive functions. Logic, Symbolic and mathematical.