Recursion Theory for Metamathematics [Hardcover]

This work is a sequel to the author'sG?del's Incompleteness Theorems, though it can be read independently by anyone familiar with G?del's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.

1. Recursive Enumerability and Recursivity
2. Undecidability and Recursive Inseparability
3. Indexing
4. Generative Sets and Creative Systems
5. Double Generativity and Complete Effective Inseparability
6. Universal and Doubly Universal Systems
7. Shepherdson Revisited
8. Recursion Theorems
9. Symmetric and Double Recursion Theorems
10. Productivity and Double Productivity
11. Three Special Topics
12. Uniform Godelization

A self-contained exposition, it presumes neither a reading of the previous volume . . . nor a prior knowledge of recursion theory. The reader with some familiarity with both recursion theory and logic should find this an excellent source for the interconnections between them. --Choice

Smullyan is not only an outstanding authority on this subject, but is also a skilled pedagogue, with a special talent for formulating simple riddles, which illuminate this very difficult and profound subject. Smullyan has made an important contribution toward the wider understanding of the work of Godel and his followers. . . . Smullyan plays a significant role in the further development of mathematical logic and the elucidation of its relation to metamathematics. He continues to be one of the foremost popularizers of the subject. --American Scientist

. . . an interesting presentation of recursion theory from the point of view of its applications in metamathematics, indicating many interrelations between various notions and properties. It willó`