The simple substitution property for superintuitionistic propositional logics and its relation to the separability property

We study the simple substitution property for superintuitionistic propositional calculi, which are axiomatizations of superintuitionistic propositional logic, and obtain an algebraic criteria for the existence of this property. This is used to prove that many logics, including almost all of those generated by formulae in one variable, do not have the simple substitution property. We obtain a series of results that establish a connection between separability and possession of this property by axiomatizations of the logics considered.