Geodesic
Arithmetical realizability and basic logic
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 52-56

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Absolute arithmetical realizability of predicate formulas is introduced. It is proved that the intuitionistic logic is not sound with this semantics, but the basic logic is sound. 
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A. Yu. Konovalov. Arithmetical realizability and basic logic. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2016), pp. 52-56. http://geodesic.mathdoc.fr/item/VMUMM_2016_1_a8/