Computability over the Partial Continuous Functionals

Journal of Symbolic Logic 65 (3):1133-1142 (2000)
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Abstract

We show that to every recursive total continuous functional $\Phi$ there is a PCF-definable representative $\Psi$ of $\Phi$ in the hierarchy of partial continuous functionals, where PCF is Plotkin's programming language for computable functionals. PCF-definable is equivalent to Kleene's S1-S9-computable over the partial continuous functionals.

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Dag Normann
University of Oslo

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References found in this work

Interpretation of analysis by means of constructive functionals of finite types.Georg Kreisel - 1959 - In A. Heyting (ed.), Constructivity in mathematics. Amsterdam,: North-Holland Pub. Co.. pp. 101--128.
Total sets and objects in domain theory.Ulrich Berger - 1993 - Annals of Pure and Applied Logic 60 (2):91-117.
Filter spaces and continuous functionals.J. M. E. Hyland - 1979 - Annals of Mathematical Logic 16 (2):101-143.

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