Computability and Logic

by George S. Boolos , John P. Burgess , Richard C. Jeffrey

• ISBN13: 9780521701464
• ISBN10: 0521701465
• Edition: 5th
• Format: Paperback
• Copyright: 2007-09-17
• Publisher: Cambridge University Press

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 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 new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This new edition is also accompanied by a website as well as an instructor's manual.

Table of Contents

Computability Theory

Enumerability

Diagonalization

Turing computability

Uncomputability

Abacus computability

Recursive functions

Recursive sets and relations

Equivalent definitions of computability

Basic Metalogic

A precis of first-order logic: syntax

A precis of first-order logic: semantics

The undecidability of first-order logic

Models

The existence of models

Proofs and completeness

Arithmetization

Representability of recursive functions

Indefinability, undecidability, incompleteness

The unprovability of consistency

Further Topics

Normal forms

The Craig interpolation theorem

Monadic and dyadic logic

Second-order logic

Arithmetical definability

Decidability of arithmetic without multiplication

Non-standard models

Ramsey's theorem

Modal logic and provability

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