Assume that is a definable group in a stable structure . Newelski showed that the semigroup of complete types concentrated on is an inverse limit of the -definable (in ) semigroups . He also showed that it is strongly -regular: for every , there exists such that is in a subgroup of . We show that is in fact an intersection of definable semigroups, so is an inverse limit of definable semigroups, and that the latter property is enjoyed by all -definable semigroups in stable structures.
"Semigroups in Stable Structures." Notre Dame J. Formal Logic 59 (3) 417 - 436, 2018. https://doi.org/10.1215/00294527-2018-0003