Diagonalization and Self-Reference

Hardcover | February 1, 1984

byRaymond M. Smullyan

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The main purpose of this book is to present a unified treatment of fixed points as they occur in Godel'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 firstchapters are of an introductory nature and consist mainly of exercises with solutions given to most of them.

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The main purpose of this book is to present a unified treatment of fixed points as they occur in Godel'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 firstchapters are of an introductory nature and c...

Raymond M. Smullyan is at Indiana University.

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Format:HardcoverDimensions:412 pages, 9.21 × 6.14 × 1.02 inPublished:February 1, 1984Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198534507

ISBN - 13:9780198534501

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Table of Contents

I Introduction to Self-Reference and Recursion1. Introduction to self-reference2. Some classical fixed point argument compared3. How to silence a universale machine4. Some general incompleteness theorems5. Self-reference in arithmetic6. Introduction to formal systems and recursion7. A universal system and its applicationsII Systems with Effective Properties8. Arithmetization of formal systems9. Elementary formal systems and incompleteness proofs10. Doubly indexed relational systems11. Effective representation systemsIII Fixed Point Theorems in a General Setting12. Sequential systems13. Strong fixed point properties14. Multiple fixed point properties15. Synchronization and pairing functions16. Some further relations between fixed point propertiesIV Combinators and Sequential systems17. Fixed point properties of combinatory logic18. Formal combinatory logic19. A second variety of fixed point theorems20. Extended sequential systems