Post complete and 0-axiomatizable modal logics
A modal logic is said to be Post complete if it has no proper consistent extensions. The Post number p(L) of a logic L is the cardinal of the set of all Post complete extensions of L. The author proves that for any n, \(1\leq n\leq 2^{\aleph_ 0}\), there exist \(2^{\aleph_ 0}\) normal modal logics with Post number equal to n. The investigation is done via the study of dual spaces of free algebras without generators over the varieties of modal algebras.
scientific article; zbMATH DE number 4164807
scientific article