Submission date: 8 September 2015

Abstract:

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 ∞-definable (in M^{eq}) semigroups S_{G,Δ}(M). He also shows that it is strongly π-regular: for every p in S_{G,Δ}(M) there exists n in N such that p^n is in a subgroup of S_{G,Δ}(M).

We show what S_{G,Δ}(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 ∞-definable semigroups in stable structures.

Mathematics Subject Classification: Primary 03C60; Secondary 03C98, 03C45

Keywords and phrases: Stable Groups, Stable Semigroups, Strong pi-regularity,

Full text arXiv 1509.02275: pdf, ps.