Kripke Models Extension For Epistemic Logic

There are several ways for de ning the notion submodelfor Kripke models of intuitionistic rst-order logic. In our approach aKripke model A is a submodel of a Kripke model B if they have thesame frame and for each two corresponding worlds A and B of them,A is a subset of B and forcing of atomic formulas with parametersin the smaller one, in A and B, are the same. In this case, B is calledan extension of A.In this paper we de ne a suitable version of the notion of homomor-phism for Kripke models of intuitionistic rst-order logic and character-ize theories that are preserved under inverse images of homomorphisms.Moreover, we de ne a notion of union of chain for Kripke models andde ne a class of formulas that is preserved in unions of chains.