Geodesic
Arithmetical realizability and primitive recursive realizability
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 60-64 
A. Yu. Konovalov. Arithmetical realizability and primitive recursive realizability. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 60-64. http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The semantics of the predicate logic based on the absolute arithmetical realizability is proved to differ from the semantics based on the primitive recursive realizability by Salehi.

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

[2] Salehi S., “Provably total functions of basic arithmetic”, Math. Log. Quart., 49:3 (2003), 316—322 | DOI | MR | Zbl

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

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

[5] Ardeshir M., “A translation of intuitionistic predicate logic into basic predicate logic”, Stud. Log., 62 (1999), 341—352 | DOI | MR | Zbl

[6] Viter D.A., Primitivno-rekursivnaya realizuemost i logika predikatov, Dep. v VINITI 06.08.2001, No 1830-V2001, M., 2001

[7] Viter D.A., Primitivno-rekursivnaya realizuemost i konstruktivnaya teoriya modelei, Kand. dis., M., 2001

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

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