Geodesic
Absolute $L$-realizability and intuitionistic logic
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 50-53 
A. Yu. Konovalov. Absolute $L$-realizability and intuitionistic logic. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2019), pp. 50-53. http://geodesic.mathdoc.fr/item/VMUMM_2019_2_a9/
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     title = {Absolute $L$-realizability and intuitionistic logic},
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Voir la notice de l'article provenant de la source Math-Net.Ru

An absolute $L$-realizability of predicate formulas is introduced for all countable extensions $L$ of the language of arithmetic. It is proved that the intuitionistic logic is not sound with this semantics.

[1] Klini S. K., Vvedenie v metamatematiku, IL, M., 1957

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

[3] Salehi S., “Primitive recursive realizability and basic arithmetic”, Bull. Symbol. Logic, 7:1 (2001), 147–148

[4] Ruitenburg W., “Basic predicate calculus”, Notre Dame J. Formal Logic, 39:1 (1998), 18–46 | DOI | MR | Zbl

[5] Konovalov A. Yu., Plisko V. E., “O giperarifmeticheskoi realizuemosti”, Matem. zametki, 98:5 (2015), 725–746 | DOI | MR | Zbl

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