An elementary construction for a non-elementary procedure

We consider the problem of the product finite model property for binary products of modal logics. First we give a new proof for the product finite model property of the logic of products of Kripke frames, a result due to Shehtman. Then we modify the proof to obtain the same result for logics of products of Kripke frames satisfying any combination of seriality, reflexivity and symmetry. We do not consider the transitivity condition in isolation because it leads to infinity axioms when taking products. © 2002 Kluwer Academic Publishers.