In 1931, Princeton mathematician Kurt Godel startled the scientific world with his 'Theorem of Undecidability', which showed that some statements in mathematics are inherently 'undecidable'. This volume of the 'Oxford Logic Guides' is a sequel to Smullyan's Godel's 'Incompleteness Theorems' (Oxford Logic Guides No. 19, 1992).

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 will certainly be studied carefully and referred to by students and specialists alike." --Roman Murawski, Mathematical Reviews "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 will certainly be studied carefully and referred to by students and specialists alike." --Roman Murawski, Mathematical Reviews