About this product

Product Identifiers

PublisherOxford University Press, Incorporated

ISBN-100195046722

ISBN-139780195046724

eBay Product ID (ePID)72357

Product Key Features

Number of Pages160 Pages

LanguageEnglish

Publication NameGodel's Incompleteness Theorems

SubjectLogic

Publication Year1992

TypeTextbook

Subject AreaMathematics

AuthorRaymond M. Smullyan

SeriesOxford Logic Guides

FormatHardcover

Dimensions

Item Height0.6 in

Item Weight15.5 Oz

Item Length9.6 in

Item Width6.3 in

Additional Product Features

Intended AudienceCollege Audience

LCCN92-016377

Reviews"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 mathematicallogic 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, "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. . . . animportant 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 thesubject." --American Scientist, "Elegant . . . the strategy . . . is highly instructive, as it casts thepurpose behind each step of the proof in high relief." --Choice, "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 ofthe '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, "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 dullnessor obscurity. His writing is clear and lively . . . . I am eagerly awaiting the sequel's appearance." --Leon Harkleroad, Modern Logic

Series Volume Number19

Table Of Content1. The General Idea Behind Gdel's Proof2. Tarski's Theorem for Arithmetic3. The Incompleteness of Peano Arithmetic with Exponentation4. Arithmetic Without the Exponential5. Gdel's Proof Based on Consistency6. Rosser Systems7. Shepherdson's Representation Theorems8. Definability and Diagonalization9. The Unprovability of Consistency10. Some General Remarks on Provability and Truth11. Self-Referential Systems

SynopsisKurt 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, guidesthe 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, conciseintroduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists., 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., 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.

LC Classification NumberQA9.65.S69 1992