拟极小预几何结构的稠密 - 余稠密扩张
Dense-codense expansions of quasiminimal pregeometry structures
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中文总结 AI 辅助
研究具有稠密 - 余稠密一元谓词的拟极小预几何结构的扩张，通过\(L_{\omega_1 \omega}(Q)\) - 句子公理化证明其\(\omega\)-稳定性，为\(H\)-结构及优美对给出独立性概念，建立预几何复杂性与扩张性质的联系。
中文摘要 AI 辅助
我们研究具有稠密 - 余稠密一元谓词的拟极小预几何结构的扩张，以及它们与基础结构预几何复杂性性质的关系。我们考虑了优美对以及\(H\)-结构。证明了这些扩张都可用单个\(L_{\omega_1 \omega}(Q)\) - 句子公理化，且都是\(\omega\)-稳定的。对于\(H\)-结构，给出了扩张中独立性的自然概念，当基础结构是模结构时，也为优美对给出了独立性的自然概念。然后将预几何的复杂性与扩张的性质联系起来。
英文摘要
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 $L_{ω_1 ω}(Q)$-sentence and that both expansions are $ω$-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.
