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Godel's Incompleteness Theorems : Oxford Logic Guides - Raymond M. Smullyan

Godel's Incompleteness Theorems

Oxford Logic Guides

Hardcover

Published: 20th August 1992
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Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.

This is a clearly written, brisk book. Advanced students will find it both a useful text and a valuable reference. It is a very complete account of the various proofs of the Goedel theorems and as such is a valuable contribution to the literature. * A.M. Coyne, Zbl. Math. 787 * 'rigorously developed, yet pedagogically sensitive; carefully structured, yet elegantly presented ... fine introductions to areas that are of central importance to contemporary classical logic and foundations of mathematics Goedel's incompleteness theorems, is noteworthy for its unusually straight-forward presentations of some of the most intellectually rewarding results proved this century' A.D. Irvine, University of British Columbia, History and Philosophy of Logic, 15 (1994)

The General Idea Behind Gdel's Proof
Tarski's Theorem for Arithmetic
The Incompleteness of Peano Arithmetic with Exponentation
Arithmetic Without the Exponential
Gdel's Proof Based on Consistency
Rosser Systems
Shepherdson's Representation Theorems
Definability and Diagonalization
The Unprovability of Consistency
Some General Remarks on Provability and Truth
Self-Referential Systems
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780195046724
ISBN-10: 0195046722
Series: Oxford Logic Guides
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 154
Published: 20th August 1992
Publisher: Oxford University Press Inc
Country of Publication: US
Dimensions (cm): 24.5 x 16.5  x 1.5
Weight (kg): 0.36