Generalized Realizability and Markov’s Principle

Abstract

Various variants of the concept of the V-realizability for predicate formulas are defined where indices of functions in the set V are used for interpreting the implication and the universal quantifier. It is proved that Markov’s principle is weakly V-realizable, not uniformly V-realizable, and uniformly V-realizable in any V-enumerable domain M ⊆ ℕ.