THE ALGEBRAIC AND KRIPKE'S SEMANTICS FOR QUANTIFIED MODAL SYSTEMS——THE CASE CONCERNING S5

In [1] and [2], the late modal logician E. J. Lemmon investigated the connexion between the algebraic and Kripke’s semantics for two series of modal propositional systems;he also pronounced in [1] that a third paper would be prepared to discuss the same connexion for quantifications of all the modal systems considered therein. Unfortunately, owing to his untimely death, this Paper did not come out. In this note we discuss the connexion