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Diagonalization and Self-Reference : Oxford Logic Guides - Raymond M. Smullyan

Diagonalization and Self-Reference

Oxford Logic Guides

Hardcover

Published: 1st September 1994
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The main purpose of this book is to present a unified treatment of fixed points as they occur in Gödel's incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. The book provides a survey of introductory material and a summary of recent research. The first chapters are of an introductory nature and consist mainly of exercises with solutions given to most of them.

"The book is devoted to a rather difficult topic; its style, however, makes most of its parts digestible, sometimes even enjoyable." -- Mathematical Reviews"Smullyan goes right to the essence of Godel's argument and its subsequent extensions. He thereby achieves a simplicity that will reach out to the general reader even as it will delight the expert." --Choice"Exhibit[s] the hallmarks of Smullyan's style. . .Accessible to beginners, yet present[s] material of interest to specialists."--Modern Logic"A highly original approach."--Journal of Symbolic Logic "The book is devoted to a rather difficult topic; its style, however, makes most of its parts digestible, sometimes even enjoyable." -- Mathematical Reviews "Smullyan goes right to the essence of Godel's argument and its subsequent extensions. He thereby achieves a simplicity that will reach out to the general reader even as it will delight the expert." --Choice "Exhibit[s] the hallmarks of Smullyan's style. . .Accessible to beginners, yet present[s] material of interest to specialists."--Modern Logic "A highly original approach."--Journal of Symbolic Logic "The book is devoted to a rather difficult topic; its style, however, makes most of its parts digestible, sometimes even enjoyable." -- Mathematical Reviews "Smullyan goes right to the essence of Godel's argument and its subsequent extensions. He thereby achieves a simplicity that will reach out to the general reader even as it will delight the expert." --Choice "Exhibit[s] the hallmarks of Smullyan's style. . .Accessible to beginners, yet present[s] material of interest to specialists."--Modern Logic "A highly original approach."--Journal of Symbolic Logic "The book is devoted to a rather difficult topic; its style, however, makes most of its parts digestible, sometimes even enjoyable." -- Mathematical Reviews"Smullyan goes right to the essence of Godel's argument and its subsequent extensions. He thereby achieves a simplicity that will reach out to the general reader even as it will delight the expert." --Choice"Exhibit[s] the hallmarks of Smullyan's style. . .Accessible to beginners, yet present[s] material of interest to specialists."--Modern Logic"A highly original approach."--Journal of Symbolic Logic

I Introduction to Self-Reference and Recursion 1: Introduction to self-reference 2: Some classical fixed point argument compared 3: How to silence a universale machine 4: Some general incompleteness theorems 5: Self-reference in arithmetic 6: Introduction to formal systems and recursion 7: A universal system and its applications II Systems with Effective Properties 8: Arithmetization of formal systems 9: Elementary formal systems and incompleteness proofs 10: Doubly indexed relational systems 11: Effective representation systems III Fixed Point Theorems in a General Setting 12: Sequential systems 13: Strong fixed point properties 14: Multiple fixed point properties 15: Synchronization and pairing functions 16: Some further relations between fixed point properties IV Combinators and Sequential systems 17: Fixed point properties of combinatory logic 18: Formal combinatory logic 19: A second variety of fixed point theorems 20: Extended sequential systems

ISBN: 9780198534501
ISBN-10: 0198534507
Series: Oxford Logic Guides
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 412
Published: 1st September 1994
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.2 x 15.8  x 2.6
Weight (kg): 0.82