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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 core mechanics and implications of Kurt Godel's incompleteness theorems, which demonstrate that formal mathematical systems contain statements that are inherently undecidable. Raymond M. Smullyan, a distinguished logician, utilizes his expertise to distill complex logical proofs into an accessible format for those with a foundational understanding of mathematical logic. The text serves as a bridge between high-level mathematical theory and the philosophical questions surrounding the limits of formal systems.
What You Will Find
Scope Limits
Experts and academics frequently cite this work as a premier introductory text for those seeking to understand the technical nuances of Godel's work without becoming overwhelmed by excessive abstraction. Readers often note that Smullyan's pedagogical approach successfully clarifies one of the most challenging topics in modern logic.
Page Count:
152
Publication Date:
1992-01-01
Publisher:
Oxford University Press
ISBN-10:
0190281448
ISBN-13:
9780190281441
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