Some results on Kripke models over an arbitrary fixed frame

摘要

We study the relations of being substructure and elementary substructure between Kripke models of intuitionistic predicate logic with the same arbitrary frame. We prove analogues of Tarski's test and Lowenheim-Skolem's theorems as determined by our definitions. The relations between corresponding worlds of two Kripke models K approx.< K' are studied.