Separable Kripke structures are algebraically universal

Abstract

For every poset \((I,\leq)\) and every family \((G_i)_{i\in I}\) of groups there exists a family of separable Kripke structures \((K_i)_{i\in I}\) on the same set, such that \(G_i\cong Aut(K_i)\) and \(K_i\) is subalgebra of \(K_j iff i\leq j, \rom {for} i, j\in I\). More generally, this work 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.