GENERIC STABILITY AND STABILITY

Abstract

AbstractWe prove two results about generically stable typespin arbitrary theories. The first, on existence of strong germs, generalizes results from [2] on stably dominated types. The second is an equivalence of forking and dividing, assuming generic stability ofp(m)for allm. We use the latter result to answer in full generality a question posed by Hasson and Onshuus: IfP(x) εS(B) is stable and does not fork overAthenprestrictionAis stable. (They had solved some special cases.)