Gödel's incompleteness theorems / Raymond M. Smullyan.

Format:

Book

Author/Creator:

Smullyan, Raymond M., author.

Series:

Oxford logic guides ; 19.

Oxford scholarship online.

Oxford logic guides ; 19

Oxford scholarship online

Language:

English

Subjects (All):

Gödel, Kurt.

Gödel's theorem.

Physical Description:

1 online resource (156 p.)

Place of Publication:

New York : Oxford University Press, 2020.

Language Note:

English

Summary:

Kurt Gödel, 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 Gödel'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 text will appeal to mathematicians, philosophers, and computer scientists.

Contents:

Contents; I: The General Idea Behind Gödel's Proof; II: Tarski's Theorem for Arithmetic; III: The Incompleteness of Peano Arithmetic With Exponentiation; IV: Arithmetic Without the Exponential; V: Gödel's Proof Based on ω-Consistency; VI: Rosser Systems; VII: Shepherdson's Representation Theorems; VIII: Definablity and Diagonalization; IX: The Unprovability of Consistency; X: Some General Remarks on Provability and Truth; XI: Self-Referential Systems; References; Index

Notes:

Previously issued in print: 1992.

Includes bibliographical references and index.

Description based on print version record and publisher information.

ISBN:

0-19-028144-8

0-19-756003-2

1-280-43982-3

9786610439829

1-4237-3519-6

0-19-536437-6

1-60129-641-X

OCLC:

228136562