Weakly one-based geometric theories

We study the class of weakly locally modular geometric theories introduced in [5], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We nd new conditions equivalent to weak local modularity: weak one-basedness and the absence of type de nable almost quasidesigns. Among other things, we show that weak one-basedness is closed under reducts and generic predicate expansions. We also show that a lovely pair expansion of a non-trivial weakly one-based ω-categorical superrosy thorn rank 1 theory interprets an in nite vector space over a nite eld.