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Computability over the partial continuous functionals

Published online by Cambridge University Press:  12 March 2014

Dag Normann
Dag Normann*
Affiliation:
Department of Mathematics, The University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway E-mail: dnormann@math.uio.no
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Abstract

We show that to every recursive total continuous functional Φ there is a PCF-definable representative Ψ of Φ 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 3 , September 2000 , pp. 1133 - 1142
Copyright
Copyright © Association for Symbolic Logic 2000

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