Intuitionistic implication without disjunction
Gerard R. Renardel de Lavalette, Lex Hendriks, Dick de Jongh

Abstract:
We investigate fragments of intuitionistic propositional logic
containing implication but not disjunction. These fragments are
finite, but their size grows superexponentially with the number of
generators. Exact models are used to characterize the fragments.

Keywords: intuitionistic logic;  implication;  exact model