The simple substitution property of the intermediate propositional logics on finite slices

We study about the intermediate propositional logics obtained from the intuitionistic propositional logics by adding some axioms. We define the simple substitution property for a set of additional axioms. Hitherto have been known only three intermediate logics that have the additional axioms with the property, and in this paper, we add one more example, that is, we give new axioms with the property to the logic Sω. Further, we decide with one among the axioms composed of one propositional variable has the property.