Admissible rules in the implication–negation fragment of intuitionistic logic

Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions (intermediate logics). A Kripke semantics characterization is given for the (hereditarily) structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis.