On representation of dynamic algebras with reversion
We investigate the role of the reversion operator in dynamic algebras. We show that all actions in a dynamic algebra with reversion are completely additive. So the considering of the reversion is a way how to axiomatize complete additivity by purely algebraic means. Our main result states that every separable *-continuous dynamic algebra with reversion can be represented as a subalgebra of a full complete dynamic algebra consisting of all completely additive functions on a complete Boolean algebra. We give some corollaries related to the problem of representability of dynamic algebras by Kripke structures. We generalize some results from dynamic algebras with reversion to dynamic algebras with completely additive actions.
Section 1 deals with basic definitions. In Section 2 we introduce and investigate invertible functions. Section 3 contains main results. In Section 4 we discuss generalizations to dynamic algebras without reversion.
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