Minimal types in super-dependent theories

Abstract

We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn-minimal types in super-rosy dependent theories of finite rank. We prove that such theories are coordinatised by thorn-minimal types and that such a type is unstable if an only if every non-algebraic extension thereof is. We conclude that a type is stable if and only if it admits a coordinatisation in thorn-minimal stable types. We also show that non-trivial thorn-minimal stable types extend stable sets.