Diagonalization and Self-Reference
Clarendon Press (Verlag)
978-0-19-853450-1 (ISBN)
This Oxford Logic Guide presents a unified treatment of fixed points, self-reference, and diagonalization as they occur in Gödel's incompleteness proofs, recursion theory, combinatory logics, semantics, and metamathematics. There is also a presentation of new results - partly in these areas, but mostly in their synthesis.
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
| Erscheint lt. Verlag | 1.9.1994 |
|---|---|
| Reihe/Serie | Oxford Logic Guides ; 27 |
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 158 x 242 mm |
| Gewicht | 778 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 0-19-853450-7 / 0198534507 |
| ISBN-13 | 978-0-19-853450-1 / 9780198534501 |
| Zustand | Neuware |
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