Diagonalization and Self-Reference

This volume's purpose is to present a unified treatment of fixed points as they occur in Godel's incompleteness proofs, recursion theory, combinatory logic, semantics and metamathematics. It provides a survey of introductory material and a summary of recent research.

Klappentext
This book presents a systematic, unified treatment of fixed points as they occur in Godel's incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. Packed with instructive problems and solutions, the book offers an excellent introduction to the subject and highlights recent research.

Zusammenfassung
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.

Inhalt
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

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