Separable Kripke structures are algebraically universal

Abstract

For every poset (I; ) and every family .Gi /i2I of groups there exists a family of separable Kripke structures .Ki /i2I on the same set, such thatGi D Aut.Ki / andKi is subalgebra ofKj iff i j , for i; j 2 I . More generally, thiswork is concerned with representations of algebraic categories by means of the category of separable Kripke structures. Consequences thereof are mentioned. Thus, in contrast to the algebraic non-universality of the category of Boolean algebras we conclude the algebraic universality of the category of separable dynamic algebras. Perfect classes of Kripke structures are introduced.