Geodesic
Dialogue interpretation of the classical predicate calculus
Izvestiya. Mathematics, Tome 61 (1997) no. 1, pp. 225-233 
V. A. Yankov. Dialogue interpretation of the classical predicate calculus. Izvestiya. Mathematics, Tome 61 (1997) no. 1, pp. 225-233. http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

An intuitionistic dialogue interpretation is constructed for the classical predicate calculus, and a completeness theorem (an intuitionistic analogue of the Godel theorem) is proved for the interpretation.

[1] Yankov V. A., “Dialogovaya teoriya dokazatelstva”, Izv. RAN. Ser. matem., 58:3 (1994), 140–178 | MR

[2] Raseva E., Sikorskii R., Matematika metamatematiki, Nauka, M., 1972, S. 343–345 | MR

[3] Spector C., “Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics”, Proceedings of the Symposia in Pure Mathematics, 5, ed. J. C. E. Dekher, Amer. Math. Soc., 1962, 1–27 | MR