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Goedel's Incompleteness Theorems


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Table of Contents

1: The General Idea Behind Gdel's Proof 2: Tarski's Theorem for Arithmetic 3: The Incompleteness of Peano Arithmetic with Exponentation 4: Arithmetic Without the Exponential 5: Gdel's Proof Based on Consistency 6: Rosser Systems 7: Shepherdson's Representation Theorems 8: Definability and Diagonalization 9: The Unprovability of Consistency 10: Some General Remarks on Provability and Truth 11: Self-Referential Systems


"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

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