Geodesic
Generalized realizability and the Markov principle
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2020), pp. 60-64 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[3] Konovalov A. Yu., “Arifmeticheskaya realizuemost i bazisnaya logika”, Vestn. Mosk. un-ta. Matem. Mekhan., 2016, no. 1, 52–56 | Zbl

[4] Plisko V. E., “Absolyutnaya realizuemost predikatnykh formul”, Izv. AN SSSP. Ser. matem., 47:2 (1983), 315–334 | MR