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Computability and logic / George S. Boolos, John P. Burgess , Richard C. Jeffrey.

By: Contributor(s): Material type: TextTextPublisher: Cambridge : Cambridge University Press, 2007Edition: Fifth editionDescription: 1 online resource (xiii, 350 pages) : digital, PDF file(s)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511804076 (ebook)
Other title:
  • Computability & Logic
Subject(s): Additional physical formats: Print version: : No titleDDC classification:
  • 511.3/52 22
LOC classification:
  • QA9.59 .B66 2007
Online resources:
Contents:
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.
Summary: 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.
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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.

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