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Part 2. Special Issues in Intellectual Systems Theory

Markov's principle is uniformly $V$-realizable in any $V$-enumerable domain

A. Yu. Konovalov


Abstract: Various variants of the notion of the $V$-realizability for predicate formulas are defined, where indexes 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 $M \subseteq \mathbb {N}$.

Keywords: constructive semantics, realizability, absolute realizability, generalized realizability, Markov's Principle.