Quasivarieties of orthomodular lattices determined by conditions on states

Abstract.

In this paper we carry on the research initiated in [13] and [14]. We consider classes of orthomodular lattices which satisfy certain state and polynomial conditions. We show that these classes form quasivarieties. We then exhibit basic examples of these quasivarieties (some of these examples originated in the quantum logic theory). We finally show how the quasivarieties in question can be described in terms of implicative equations. (It should be noted that in some cases we have not been able to clarify whether or not a class shown to be a quasivariety is a variety, see Section 2.)