Submission date: 17 December 2008.

Abstract:

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.

Mathematics Subject Classification: 03C45, 03C64

Keywords and phrases: geometric structures, linear structures, rosy theories, o-minimal theories, dense pairs, lovely pairs.

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