Geodesic
Dialogue interpretation of the classical predicate calculus
Izvestiya. Mathematics , Tome 61 (1997) no. 1, pp. 225-233.

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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. 
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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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[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