Diagonalization and Self-Reference
Published on 1. September 1994
Book
Hardback
412 pages
978-0-19-853450-1 (ISBN)
Description
The main purpose of this book is to present a unified treatment of fixed points as they occur in Goedel'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.
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
Professional and scholarly
Dimensions
Height: 242 mm
Width: 158 mm
Thickness: 26 mm
Weight
778 gr
ISBN-13
978-0-19-853450-1 (9780198534501)
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Schweitzer Classification
Person
Content
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