“…Corresponding questions for classes of M-acts over a monoid M have been answered in [10,19,1] and [11], see also the survey article [12]. The classes of projective (strongly flat, po-flat, weakly po-flat) left S-posets Pr(SF , PF , WPF ) have recently been considered in [15] (which uses slightly different terminology; the results also appearing in [16]) as has the class F r of free left S-posets in the case where S has only finitely many right ideals. We note that many of the techniques of [15] follow those in the M-act case and, for this reason, we aim here to produce two general strategies that will deal with a number of axiomatisability questions for classes of S-posets (and, with minor adjustment, M-acts).…”