Weakly one-based geometric theories
Résumé
We study the class of weakly locally modular geometric theories introduced in \cite{BeVa}, 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 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 $\omega$-categorical superrosy thorn rank 1 theory interprets an infinite vector space over a finite field.
Domaines
Logique [math.LO]
Origine : Fichiers produits par l'(les) auteur(s)
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