Mathematical Logic Quarterly

Complements of Intersections in Constructive Mathematics

Journal Article

Abstract

We examine, from a constructive perspective, the relation between the complements of S, T, and ST in X, where X is either a metric space or a normed linear space. The fundamental question addressed is: If x is distinct from each element of ST, if s ϵ S, and if t ϵ T, is x distinct from s or from t? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle and the completeness of metric spaces.

Mathematics Subject Classification: 03F65, 46S30.

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