Submission date: 15 March 2010.

Abstract:

We study the class of weakly locally modular geometric theories introduced in [5], a common generalization of linear SU rank 1 and linear o-minimal theories. We find new conditions equivalent to weak local modularity: weak one-basedness and the absence of type-definable 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 infinite vector space over a finite field.

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