The canonical base property (CBP) is a property of finite rank theories, which was introduced by Pillay and whose formulation was motivated by results of Campana in complex geometry. The main feature of such a property is that it provides a dichotomy for types of rank one, and in consequence one can reproduce Hrushovski’s proof of Mordell-Lang for function fields in characteristic zero with considerable simplifications.In this talk, I will motivate (via Mordell-Lang) the statement of the CBP and describe some results around the CBP, in particular on definable groups.
- Séminaire Géométrie et théorie des modèles