The classificatiion of structures interpretable in o-minimal theories

We survey the classification of structures interpretable in o-minimal theories in terms of thorn-minimal types. We show that a necessary and sufficient condition for such a structure to interpret a real closed field is that it has a non-locally modular unstable type. We also show that assuming Zilber's Trichotomy for strongly minimal sets interpretable in o-minimal theories, such a structure interprets a pure algebraically closed field iff it has a global stable non-locally modular type. Finally, if time allows, we will discuss reasons to believe in Zilber's Trichotomy in the present context