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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.
This book investigates the fundamental limitations of formal mathematical systems as established by Kurt Godel's incompleteness theorems. Raymond M. Smullyan, a distinguished logician, utilizes his expertise to distill complex logical proofs into an accessible framework. By focusing on the mechanics of undecidability and consistency, the author provides a structured path for readers to comprehend how these theorems fundamentally altered the landscape of modern mathematics and logic.
What You Will Find
Experts frequently cite this work as a highly accessible entry point into the dense field of mathematical logic. Readers often note that while the subject matter is inherently challenging, Smullyan's pedagogical approach successfully clarifies abstract concepts for students and professionals alike.
Page Count:
160
Publication Date:
1992-08-20
Publisher:
Oxford University Press
ISBN-10:
0195046722
ISBN-13:
9780195046724
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