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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