An Introduction to Gödel's Theorems

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An Introduction to Gödel's Theorems

By Peter Smith

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In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book - extensively rewritten for its second edition - will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

Subject: Mathematics & Statistics -> Post-Calculus -> Logic

An Introduction to Gödel's Theorems
2nd edition
Publisher: Cambridge University Press 2/21/13
Imprint: Cambridge University Press
Language: English

ISBN 10: 1107326826
ISBN 13: 9781107326828
Print ISBN: 9781107022843

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