http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
1 online resource (xii, 277 pages) : illustrations
This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. Although aiming basically at a theory of higher order computability, attention is restricted to second order functionals, where the arguments are numerical functions and the values, when defined, are natural numbers. This theory is somewhat special, for to some extent it can be reduced to first order theory, but when properly extended and relativized it requires the full machinery of higher order computations. In the theory of recursive monotonic functionals the author formulates a reasonable notion of computation which provides the right frame for what appears to be a convincing form of the extended Church's thesis. At the same time, the theory provides sufficient room to formulate the classical results that are usually derived in terms of singular functionals. Presented are complete proofs of Gandy's selector theorem, Kleene's theorem on hyperarithmetical predicates, and Grilliot's theorem on effectively discontinuous functionals.
Front Cover; Recursive Functionals; Copyright Page; Contents; Preface; Chapter 1. Mappings and Domains; Chapter 2. Functionals and Predicates; Chapter 3. Basic Operations; Chapter 4. Primitive Recursive Operations; Chapter 5. Basic Recursion; Chapter 6. Church's Thesis; Chapter 7. Functional Recursion; Chapter 8. Recursive Algorithms; Chapter 9. Formalization: Structural Semantics; Chapter 10. Formalization: Reductional Semantics; Chapter 11. Interpreters; Chapter 12. A Universal Interpreter; Chapter 13. Enumeration; Chapter 14. Continuous Functionals; Chapter 15. A Selector Theorem
Chapter 16. HyperenumerationChapter 17. Recursion in Normal Classes; Appendix Recursion and Church's Thesis; References; Index; List of Symbols
Includes bibliographical references (pages 265-267) and index.
Amsterdam ; New York : North-Holland, 1992
Studies in logic and the foundations of mathematics ; v. 131
122102:125822 Elsevier Science & Technology