Geodesic
Generalized realizability and the Markov principle
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2020), pp. 60-64

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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 $M \subseteq \mathbb N$. 
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     author = {A. Yu. Konovalov},
     title = {Generalized realizability and the {Markov} principle},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_1_a8/}
}
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A. Yu. Konovalov. Generalized realizability and the Markov principle. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2020), pp. 60-64. http://geodesic.mathdoc.fr/item/VMUMM_2020_1_a8/