Computability over the partial continuous functionals

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...

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Bibliographic Details
Published in:The Journal of symbolic logic 2000-09, Vol.65 (3), p.1133-1142
Main Author: Normann, Dag
Format: Article
Language:English
Subjects:
Computability
Conceptual hierarchies
Induction assumption
Logical theorems
Mathematical functions
Mathematical logic
Mathematical theorems
Mathematics
Natural numbers
Programming languages
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Summary: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.
ISSN:0022-4812
1943-5886
DOI:10.2307/2586691