## Weakly one-based geometric theories.(English)Zbl 1405.03077

Summary: 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 conditions equivalent to weak local modularity: “weak one-basedness”, absence of type definable “almost quasidesigns”, and “generic linearity”. Among other things, we show that weak one-basedness is closed under reducts. We also show that the lovely pair expansion of a non-trivial weakly one-based $$\omega$$-categorical geometric theory interprets an infinite vector space over a finite field.

### MSC:

 03C45 Classification theory, stability, and related concepts in model theory 03C64 Model theory of ordered structures; o-minimality
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### References:

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