LetSKP be the intermediate prepositional logic obtained by adding toI (intuitionistic p.l.) the axiom schemes:S = (( ) ) (Scott), andKP = ()()() (Kreisel-Putnam). Using Kripke's semantics, we prove:1) SKP has the finite model property; 2) SKP has the disjunction property. In the last section of the paper we give some results about Scott's logic S = I+S.

For intermediate logics, there is obtained in the paper an algebraic equivalent of the disjunction propertyDP. It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP. Introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems.