David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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  and , the Kleene-Kreisel countable functionals and the hereditary effective operations (HEO) are easily characterized
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Giuseppe Longo (1988). On Church's Formal Theory of Functions and Functionals. Annals of Pure and Applied Logic 40 (2):93-133.
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