ON NON-FINITE AXIOMATIZABILITY OF n-MODAL LOGICS BETWEEN AND FOR FINITE
Let We show that any n-modal logic between and is not axiomatizable by a set of modal formulas containing finitely many propositional formulas. This is proved algebraically by showing that the corresponding variety of modal algebras, namely, that of diagonal free cylindric algebras of dimension n has no equational axiomatization using finitely many variables.
modal logic, products of uni-modal logics, finite axiomatization, diagonal-free cylindric algebras.