Journal of Symbolic Logic 49 (4):1319-1332 (1984)

A type-structure of partial effective functionals over the natural numbers, based on a canonical enumeration of the partial recursive functions, is developed. These partial functionals, defined by a direct elementary technique, turn out to be the computable elements of the hereditary continuous partial objects; moreover, there is a commutative system of enumerations of any given type by any type below (relative numberings). By this and by results in [1] and [2], the Kleene-Kreisel countable functionals and the hereditary effective operations (HEO) are easily characterized
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DOI 10.2307/2274281
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References found in this work BETA

Effective Operations on Partial Recursive Functions.J. Myhill & J. C. Shepherdson - 1955 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 1 (4):310-317.
Effective Operations on Partial Recursive Functions.J. Myhill & J. C. Shepherdson - 1955 - Mathematical Logic Quarterly 1 (4):310-317.

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On Church's Formal Theory of Functions and Functionals.Giuseppe Longo - 1988 - Annals of Pure and Applied Logic 40 (2):93-133.
A Categorical Approach to the Theory of Computation.Philip S. Mulry - 1989 - Annals of Pure and Applied Logic 43 (3):293-305.
The Computational Power of ℳω.Dag Normann & Christian Rørdam - 2002 - Mathematical Logic Quarterly 48 (1):117-124.

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