Geodesic
Kripke Models for Intuitionistic Theories with Decidable Atomic Formulas
Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 3

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Some intuitionistic theories, notably Heyting's Arithmetic, have decidable atomic formulas. We show that in Kripke models of such theories, classical structures at the nodes of a Kripke model satisfy a significant fragment of corresponding theories. In particular, all consequences which are in prenex normal form hold classically.
Classification : 03B50 03C40 
Zoran Marković. Kripke Models for Intuitionistic Theories with Decidable Atomic Formulas. Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 3 . http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a0/
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     title = {Kripke {Models} for {Intuitionistic} {Theories} with {Decidable} {Atomic} {Formulas}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {3 },
     year = {1984},
     volume = {_N_S_36},
     number = {50},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a0/}
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