  Assume $G$ is a definable group in a stable structure $M$. Newelski showed
that the semigroup $S_G(M)$ of complete types concentrated on $G$ is an inverse
limit of the $\infty$-definable (in $M^{eq}$) semigroups $S_{G,\Delta}(M)$. He
also shows that it is strongly $\pi$-regular: for every $p\in S_{G,\Delta}(M)$
there exists $n\in\mathbb{N}$ such that $p^n$ is in a subgroup of
$S_{G,\Delta}(M)$. We show that $S_{G,\Delta}(M)$ is in fact an intersection of
definable semigroups, so $S_G(M)$ is an inverse limit of definable semigroups
and that the latter property is enjoyed by all $\infty$-definable semigroups in
stable structures.
