‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivit...

Let C be a class of ordered algebras of a given fixed type τ . Associated with the type is a first order language Lτ , which must also contain a binary predicate to be interpreted by the ordering in members of C. One can then ask the question, when is the class C axiomatisable by sentences of Lτ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a ...

‎‎‎In this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $S$-posets‎, ‎posets with a monotone action of a‎ pomonoid $S$ on them‎, ‎is studied‎. ‎We give a criterion‎, ‎like the Baer condition for injectivity of modules‎, ‎or Skornjakov criterion for injectivity of $S$-sets‎, ‎for the order dense injectivity‎. ‎Also‎, ‎we consider such injectivit...

Let C be a class of ordered algebras of a given fixed type τ . Associated with the type is a first order language Lτ , which must also contain a binary predicate to be interpreted by the ordering in members of C. One can then ask the question, when is the class C axiomatisable by sentences of Lτ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a ...

In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are ...