Dense-codense expansions of quasiminimal pregeometry structures

Alexander Berenstein; Evgueni Vassiliev

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arXiv · 2607.11619

Dense-codense expansions of quasiminimal pregeometry structures

Alexander Berenstein·Evgueni Vassiliev

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Abstract

We study expansions of quasiminimal pregeometry structures with a dense codense unary predicate and their relation with the complexity properties of the pregeometry of the underlying structure. We consider beautiful pairs as well as $H$-structures. We show each of these expansions can be axiomatized with a single $L_{\omega_1 \omega}(Q)$-sentence and that both expansions are $\omega$-stable. For $H$-structures we provide a natural notion of independence in the expansion and when the underlying structure is modular, we also provide a natural notion of independence for beautiful pairs. Then we relate the complexity of the pregeometry to properties of the expansions.

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BibTeX RIS

Alexander Berenstein, Evgueni Vassiliev. 2026-07-13. Dense-codense expansions of quasiminimal pregeometry structures. https://arxiv.org/abs/2607.11619

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