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Article · Lobachevskii Journal of Mathematics · April 1, 2021

$${P}^{{*}}$$-Combinations of Almost $${\omega}$$-Categorical Weakly o-Minimal Theories

B. Sh. Kulpeshov, Sergey Vladimirovich Sudoplatov

Beibut Kulpeshov
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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.

Advanced Topology and Set TheoryRings, Modules, and AlgebrasLimits and Structures in Graph Theoryo-minimality

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