BL An introduction to the topic - pitched at an elementary level 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.

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