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Generalized realizability and the Markov principle

A. Yu. Konovalov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Various variants of the notion 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 $M \subseteq \mathbb N$.

Key words: constructive semantics, realizability, absolute realizability, generalized realizability, Markov's principle.

UDC: 510.25; 510.64

Received: 11.07.2018

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2020, 75:1, 38–41

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