Goedel's Incompleteness Theorems

Goedel's Incompleteness Theorems

4.42 (45 ratings by Goodreads)
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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.
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Product details

  • Hardback | 154 pages
  • 160.02 x 236.22 x 15.24mm | 385.55g
  • New York, United States
  • English
  • 0195046722
  • 9780195046724
  • 302,352

Table of contents

1. The general idea behind Godel's proof ; 2. Tarski's theorem for arithmetic ; 3. The incompleteness of peano arithmetic with exponentation ; 4. Arithmetic without the exponential ; 5. Godel'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
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Review quote

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 Goedel theorems and as such is a valuable contribution to the literature. * A.M. Coyne, Zbl. Math. 787 * '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 Goedel'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)
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Rating details

45 ratings
4.42 out of 5 stars
5 51% (23)
4 40% (18)
3 9% (4)
2 0% (0)
1 0% (0)
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