ABSTRACT
S. Miura [4] proved that the intersection of any two finitely axiomatizable intermediate prepositional logics is finitely axiomatizable. Here we establish that this result cannot be transferred to the predicate case. We use S. Ghilardi’s functor semantics [1] generalizing standard Kripke semantics for predicate logics. Weaker generalizations of Kripke semantics [6] are not sufficient, here and so we obtain some new examples of predicate logics which are incomplete in Kripke semantics and its generalizations.
