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.

Location: http://mech.math.msu.su/~fpm/eng/k08/k087/k08707h.htm

Last modified: June 25, 2009