Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt över 249 kr.
Beskrivning
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.
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
