CHAINS OF KRIPKE MODELS

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 A® and B® of them, A® is a classical submodel of B®. In this case, B is called an extension of A. We characterize formulas that are preserved under taking extensions of Kripke models. We also define a notion of union of chain for Kripke models and introduce a class of formulas that is preserved in unions of chains.