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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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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description 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.
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ispartof The Journal of symbolic logic, 2000-09, Vol.65 (3), p.1133-1142
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1943-5886
language eng
recordid cdi_projecteuclid_primary_oai_CULeuclid_euclid_jsl_1183746172
source JSTOR Archival Journals and Primary Sources Collection
subjects Computability
Conceptual hierarchies
Induction assumption
Logical theorems
Mathematical functions
Mathematical logic
Mathematical theorems
Mathematics
Natural numbers
Programming languages
title Computability over the partial continuous functionals
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