Submission date: 16 October 2012

Abstract:

We try to analyse general invariant types in dp-minimal theories in terms of finitely satisfiable and definable ones. We prove in particular that an invariant dp-minimal type is either finitely satisfiable or definable and that a definable version of the (p,q)-theorem holds in dp-minimal theories of small or medium directionality. In an appendix with Sergei Starchenko, we prove that in dp-minimal theories with Skolem functions, every non-forking formula extends to a definable type.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1210.4479: pdf, ps.