# Weak One-Basedness

@article{Boxall2013WeakO, title={Weak One-Basedness}, author={Gareth Boxall and David Bradley-Williams and Charlotte Kestner and Alexandra Omar Aziz and Davide Penazzi}, journal={Notre Dame J. Formal Log.}, year={2013}, volume={54}, pages={435-448} }

We study the notion of weak one-basedness introduced in recent work of Berenstein and Vassiliev. Our main results are that this notion characterises linearity in the setting of geometric þ-rank 1 structures and that lovely pairs of weakly one-based geometric þ-rank 1 struc- tures are weakly one-based with respect to þ-independence. We also study geometries arising from infinite dimensional vector spaces over division rings.

## 2 Citations

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Abstract We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We find new…

### Geometric structures with a dense independent subset

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We study a generalization of the expansion by an independent dense set, introduced by Dolich, Miller, and Steinhorn in the o-minimal context, to the setting of geometric structures. We introduce the…

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