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Recursive functionals

Author: Luis E Sanchis
Publisher: Amsterdam ; New York : North-Holland, 1992.
Series: Studies in logic and the foundations of mathematics, v. 131.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Sanchis, Luis E.
Recursive functionals.
Amsterdam ; New York : North-Holland, 1992
(DLC) 92010555
(OCoLC)25628698
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Luis E Sanchis
ISBN: 9780444894472 0444894470 9780080887173 0080887171 1281778834 9781281778833
OCLC Number: 316566833
Description: 1 online resource (xii, 277 pages) : illustrations.
Contents: Mappings and Domains. Functionals and Predicates. Basic Operations. Primitive Recursive Operations. Basic Recursion. Church's Thesis. Functional Recursion. Recursive Algorithms. Formalization: Structural Semantics. Formalization: Reductional Semantics. Interpreters. A Universal Interpreter. Enumeration. Continuous Functionals. A Selector Theorem. Hyperenumeration. Recursion in Normal Classes. Recursion and Church's Thesis. References. Index.
Series Title: Studies in logic and the foundations of mathematics, v. 131.
Responsibility: Luis E. Sanchis.

Abstract:

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.

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