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  1.  21
    From Forcing to Satisfaction in Kripke Models of Intuitionistic Predicate Logic.Maryam Abiri, Morteza Moniri & Mostafa Zaare - 2018 - Logic Journal of the IGPL 26 (5):464-474.
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  2.  23
    Preservation Theorems for Kripke Models.Morteza Moniri & Mostafa Zaare - 2009 - Mathematical Logic Quarterly 55 (2):177-184.
    There are several ways for defining the notion submodel for Kripke models of intuitionistic first-order logic. In our approach a Kripke model A is a submodel of a Kripke model B if they have the same frame and for each two corresponding worlds Aα and Bα of them, Aα is a subset of Bα and forcing of atomic formulas with parameters in the smaller one, in A and B, are the same. In this case, B is called an extension of (...)
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  3.  28
    Extensions of Kripke Models.Mostafa Zaare - 2017 - Logic Journal of the IGPL 25 (5):697-699.
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  4.  21
    Homomorphisms and Chains of Kripke Models.Morteza Moniri & Mostafa Zaare - 2011 - Archive for Mathematical Logic 50 (3-4):431-443.
    In this paper we define a suitable version of the notion of homomorphism for Kripke models of intuitionistic first-order logic and characterize theories that are preserved under images and also those that are preserved under inverse images of homomorphisms. Moreover, we define a notion of union of chain for Kripke models and define a class of formulas that is preserved in unions of chains. We also define similar classes of formulas and investigate their behavior in Kripke models. An application to (...)
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    Forcing and Satisfaction in Kripke Models of Intuitionistic Arithmetic.Maryam Abiri, Morteza Moniri & Mostafa Zaare - 2019 - Logic Journal of the IGPL 27 (5):659-670.
    We define a class of first-order formulas $\mathsf{P}^{\ast }$ which exactly contains formulas $\varphi$ such that satisfaction of $\varphi$ in any classical structure attached to a node of a Kripke model of intuitionistic predicate logic deciding atomic formulas implies its forcing in that node. We also define a class of $\mathsf{E}$-formulas with the property that their forcing coincides with their classical satisfiability in Kripke models which decide atomic formulas. We also prove that any formula with this property is an $\mathsf{E}$-formula. (...)
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