Continuality of the set of maximal superintuitionistic logics with the disjunction property (Q1311077)

A superintuitionistic logic is a logic containing intuitionistic logic. Here the author treats only consistent superintuitionistic propositional logics, that is, the intermediate propositional logics. The disjunction property for a logic says that if ``\(A\) or \(B\)'' belongs to the logic, then either \(A\) or \(B\) belongs to it. In this paper, the cardinality of the maximal intermediate logics with the disjunction property is studied and as the Main Theorem, it is proved that there are a continuum of such maximal logics. Besides the Main Theorem, this note presents good information around the problem.