An Introduction to Godel's Theorems (Paperback)
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Short Description for An Introduction to Godel's Theorems A clear and accessible treatment of Godel's famous, intriguing, but much misunderstood incompleteness theorems, extensively revised in a second edition.
- Published: 31 May 2013
- Format: Paperback 402 pages
- ISBN 13: 9781107606753 ISBN 10: 1107606756
- Sales rank: 241,741
Full description for An Introduction to Godel's Theorems
In 1931, the young Kurt Godel 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. Godel 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.