Abstract

We study \(P^{*}\)-combinations of almost \(\omega\)-categorical weakly o-minimal theories. One of natural questions in the study of such a combination is the question of preserving or weakening certain properties of initial theories. Earlier, criteria for Ehrenfeuchtness of \(P^{*}\)-combinations of countably many \(\omega\)-categorical ordered theories were obtained. Here we prove that if a \(P^{*}\)-combination of countably many models of almost \(\omega\)-categorical weakly o-minimal theories preserves weak o-minimality then it also preserves almost \(\omega\)-categoricity.

中文翻译：

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$${P}^{{*}}$$ - 几乎 $${\omega}$$ -Categorical Weakly o-Minimal Theories 的组合

摘要

我们研究\(P^{*}\) - 几乎\(\omega\) -分类弱 o 极小理论的组合。研究这种组合的自然问题之一是保留或削弱初始理论的某些特性的问题。早些时候，获得了\(P^{*}\) - 可数许多\(\omega\) -分类有序理论的组合的Ehrenfeuchtness 标准。在这里我们证明，如果一个\(P^{*}\) -几乎\(\omega\) -categorical 弱 o-minimal 理论的可数许多模型的组合保持弱 o-minimalality 那么它也几乎保持\(\omega\) \) -类别。