Exact real number computations relative to hereditarily total functionals

Authors:
Dag Normann
Affiliations:
Department of Mathematics, The University of Oslo, P.O. Box 1053, Blindern N-0316 Oslo, Norway
Venue:
Theoretical Computer Science
Year:
2002

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Abstract

We show that the continuous existential quantifier ∃ω is not definable in Escardó's Real-PCF from all functionals equivalent to a given total one in a uniform way. We further prove that relative to any total functional of type (I → I) → I which gives the maximum-value for any total input, we may, given a computable, total functional φ of type (R → R) → R find a Real-PCF-definable total Ψ equivalent to φ.