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This is the second in a series of articles surveying the body of work on themodel theory of S-acts over a monoid S. The first concentrated on the theory ofregular S-acts. Here we review the material on model-theoretic properties offree, projective, and (strongly, weakly) flat S-acts. We consider questions ofaxiomatizability, completeness, model completeness, and stability for theseclasses. Most but not all of the results have already appeared; we remark thatthe description of those monoids S such that the class of free left S-acts isaxiomatizable, is new.

Model-theoretic properties of free, projective, and flat S-acts