Recursion Theory [Hardcover]

A clear and focused introduction to recursion theory that is ideal for teaching and self-study.An introduction to recursion theory that will prepare the reader for the study of advanced monographs and the current literature on the topic. The clarity and focus of this text makes it an ideal instrument for teaching and self-study.An introduction to recursion theory that will prepare the reader for the study of advanced monographs and the current literature on the topic. The clarity and focus of this text makes it an ideal instrument for teaching and self-study.Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the first publication in the Lecture Notes in Logic series, Shoenfield gives a clear and focused introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. This introduction is an ideal instrument for teaching and self-study that prepares the reader for the study of advanced monographs and the current literature on recursion theory.1. Computability; 2. Functions and relations; 3. The basic machine; 4. Macros; 5. Closure properties; 6. Definitions of recursive functions; 7. Codes; 8. Indices; 9. Church's thesis; 10. Word problems; 11. Undecidable theories; 12. Relative recursion; 13. The arithmetical hierarchy; 14. recursively enumerable relations; 15. Degrees; 16. Evaluation of degrees; 17. Large RE sets; 18. Functions of reals; 19. The analytical hierarchy; 20. The projective hierarchy; Suggestions for further reading; Index.