About regular S-posets

The concept of regular S-poset is generalization of the concept of regular S-set. The description of monoids S with axiomatizable, complete and model complete classes of regular S-posets were considered in the papers of E. V. Ovchinnikova and A. A. Stepanova. The similar questions for partially ordered monoids and S-posets were investigated in this work. The main result of the work is a description of partially ordered monoids S with axiomatizable class of regular S-posets. Besides we prowed that there does not exist S-posets with complete or model complete classes of regular S-poset.