Overview

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.

Full Product Details

Author:   Raymond M. Smullyan (Professor of Philosophy, Professor of Philosophy, Indiana University)
Publisher:   Oxford University Press
Imprint:   Clarendon Press
Volume:   27
Dimensions:   Width: 15.80cm , Height: 2.60cm , Length: 24.20cm
Weight:   0.778kg
ISBN:  

9780198534501

ISBN 10:   0198534507
Pages:   412
Publication Date:   01 September 1994
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
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Table of Contents

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

Reviews

The book is devoted to a rather difficult topic; its style, however, makes most of its parts digestible, sometimes even enjoyable. -- Mathematical Reviews<br> 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<br> Exhibit[s] the hallmarks of Smullyan's style. . .Accessible to beginners, yet present[s] material of interest to specialists. --Modern Logic<br> A highly original approach. --Journal of Symbolic Logic<br>

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