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An Introduction to Godel's Theorems

Both in the Mathematics Department Peter SmithPeter Smith

出版	Cambridge University Press, 2013
主題	Mathematics / LogicPhilosophy / Logic
ISBN	11073365899781107336582
URL	http://books.google.com.hk/books?id=W2azoQEACAAJ&hl=&source=gbs_api

註釋

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."