$P$-stability of some classes of $S$-acts

The notion of $P$-stability is a particular case of the generalized stability of complete theories. This paper discusses some problems that are related to the $P$-stability of certain classes of $S$-acts. In particular, we describe the monoids $S$ over which the classes of free, projective, strongly flat, divisible, regular $S$-acts are $P$-stable.