Hierarchies of total functionals over the reals

Authors:
Dag Normann
Affiliations:
Department of Mathematics, The University of Oslo, P.O. Box 1053, Blindern, Oslo N-0316, Norway
Venue:
Theoretical Computer Science - Logic, semantics and theory of programming
Year:
2004

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Abstract

We compare two natural constructions, the A-hierarchy and the R-hierarchy, of hereditarily total, continuous and extensional functionals of finite types over the reals. The A-hierarchy is based on the closed interval domain representation of the reals while the R-hierarchy is based on the binary negative digit representation. We show that the two hierarchies share a common maximal core. To this end, we construct an alternative to the R-hierarchy and prove a density theorem for this alternative hierarchy.