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An Introduction to Gödel's Theorems
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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 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.
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Cambridge University Press; July 2007
377 pages; ISBN 9780511346293
Read online, or download in secure PDF format
377 pages; ISBN 9780511346293
Read online, or download in secure PDF format
Subject categories
- Academic > Mathematics > General > Logic, Symbolic and mathematical
- Academic > Mathematics > General > Recursion theory
- Academic > Mathematics > General > Godel's theorem
- Academic > Mathematics > Instruments and machines
- Academic > Mathematics > Analytic mechanics
- Academic > Logic > Recursion theory
- Academic > Logic > Godel's theorem
- Academic > Computer Science
- Philosophy > Logic
- Mathematics > Logic
ISBNs
0511346298
9780511346293
9780521857840