Variations on realizability: realizing the propositional axiom of choice

Authors:
J. M. E. Hyland
Affiliations:
D. P. M. M. S. University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, U.K.
Venue:
Mathematical Structures in Computer Science
Year:
2002

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Abstract

Realizability and related functional interpretations provide models for constructive mathematics. Generally, these models do not validate the axiom of choice for propositions taken over hierarchies of extensional functionals. We describe simple classes of models where the axiom is validated.