On the existence of alternative Skolemization methods

Abstract

It is shown that no intermediate predicate logic that is sound and complete with respect to a class of frames, admits a strict alternative Skolemization method. In particular, this holds for intuitionistic predicate logic and several other well–known intermediate predicate logics. The result is proved by showing that the class of formulas without strong quantifiers as well as the class of formulas without weak quantifiers is sound and complete with respect to the class of constant domain Kripke models.