Overview
"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."
Full Product Details
Author: Raymond M. Smullyan (Professor, City College, Professor, City College, City University of New York, USA)
Publisher: Oxford University Press Inc
Imprint: Oxford University Press Inc
Volume: 19
Dimensions:
Width: 16.20cm
, Height: 1.80cm
, Length: 24.30cm
Weight: 0.435kg
ISBN: 9780195046724
ISBN 10: 0195046722
Pages: 160
Publication Date: 22 October 1992
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: To order
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Reviews
'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 Godel'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) 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 Godel theorems and as such is a valuable contribution to the literature. A.M. Coyne, Zbl. Math. 787
"""A delightful introduction to the Godel incompleteness theorems and related results. . . . reader is treated to a series of careful formulations and proofs of the central results, always with a high degree of generality and insight. The author has superbly combined his unique presentation of the 'big picture' with an appreciation of detail and rigor. Even readers who are already familiar with the incompleteness results will enjoy and benefit from this book."" --Mathematical Reviews ""Elegant . . . the strategy . . . is highly instructive, as it casts the purpose behind each step of the proof in high relief."" --Choice ""Combines scholarly contributions with the flavor of his popular works. Smullyan is not only an outstanding authority on this subject, but also a skilled pedagogue, with a special talent for formulating simple riddles, which illuminate this very difficult and profound subject. . . . an important contribution toward the wider understanding of the work of Godel and his followers. . . . Smullyan plays a significant role in the further development of mathematical logic and the elucidation of its relation to metamathematics. He continues to be one of the foremost popularizers of the subject."" --American Scientist ""Smullyan lives up to his aims. The book provides a highly accessible, user-friendly introduction to incompleteness. . . . the treatment is rigorous and contains material that even a professional logician can find informative and interesting. . . . Smullyan never confuses rigor with dullness or obscurity. His writing is clear and lively . . . . I am eagerly awaiting the sequel's appearance."" --Leon Harkleroad, Modern Logic"
