Finite axiomatizability of locally tabular superintuitionistic logics (Q581390)

A superintuitionistic propositional logic L is called locally tabular if every finite set of propositional variables generates a finite number of L-nonequivalent propositional formulae. Using the algebraic approach, being mostly the only appropriate one in such cases, the author obtains the following interesting result: if L is a finitely axiomatizable locally tabular superintuitionistic propositional logic, then L is hereditarily finitey axiomatizable iff L has not more than a denumerable set of extensions.