Action-type axiomatizable classes of group representations

The paper adjoins the book B.Plotkin, S.Vovsi "Varieties of representations of groups", Riga, "Zinatne", 1983, and turns to be, in a sense, its continuation. In the book the varieties of representations had been considered. In the matter of fact, the varieties under consideration are action-type varieties. This paper studies other classes of representations, axiomatizable in the special action-type logic.