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On some models of modal logics

The purpose of this note is to show that the models of the modal logics M, S4, Brouwersche and S5 defined by Drake in [l], following McKinsey [3], can be presented as models of the type defined by Kripke in [2]. Models based on a Boolean algebra 91 were defined in [l] as follows. A model is a triple (U,D, S) where U is a Boolean algebra, D is a maximal additive ideal of % and S is a set of operators defined on elements of 51 satisfying