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.
|Original language||English GB|
|State||Published - 2007|
- Mathematics - Logic