Mostafa Zaare

There are several ways to define the notion of 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 the frame of A is a subframe of the frame of B and for each two corresponding worlds Aα and Bα of them, Aα is a classical submodel of Bα. In this case, B is called an extension of A. We characterize formulas that are preserved under taking extensions of Kripke models. © The Author 2017. Published by Oxford University Press. All rights reserved.

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 intuitionistic first-order arithmetic is also given. © 2010 Springer-Verlag.