On lovely pairs of geometric structures

We study the theory of lovely pairs of geometric structures, in particular o-minimal structures. We characterize "linear" theories in terms of properties of the corresponding theory of the lovely pair. For o-minimal theories, we use Peterzil-Starchenko's trichotomy theorem to characterize for sufficiently general points, the local geometry around it in terms of the thorn U rank of its type.

• Type: Journal
• Year: 2010
• Where: APAL
• Authors: Alexander Berenstein, Evgueni Vassiliev
• Keywords: APAL 2010, Geometric Structures, Lovely Pair, Particular O-minimal Structures