FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 7, PAGES 63-110

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

V. Gould
A. V. Mikhalev
E. A. Palyutin
A. A. Stepanova

Abstract

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

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Last modified: June 25, 2009