Hereditarily Structurally Complete Superintuitionistic Deductive Systems

The paper studies hereditarily complete superintuitionistic deductive systems, that is, the deductive system which logic is an extension of the intuitionistic propositional logic. It is proven that for deductive systems a criterion of hereditary structurality - similar to one that exists for logics - does not exists. Nevertheless, it is proven that many standard superintuitionistic logics (including Int) can be defined by a hereditarily structurally complete deductive system.