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Article · Lobachevskii Journal of Mathematics · April 1, 2026

Pseudo-Uncountably-Categorical Structures and Theories

B. Sh. Kulpeshov, In. I. Pavlyuk, Sergey Vladimirovich Sudoplatov

Beibut Kulpeshov
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Abstract

We describe some possibilities of approximations by $$\omega_{1}$$ -categorical structures and theories. The obtained results of approximations are called pseudo- $$\omega_{1}$$ -categorical. Possibilities for expansions and restrictions of theories with respect to the $$\omega_{1}$$ -categoricity and pseudo- $$\omega_{1}$$ -categoricity are studied. We describe properties and possibilities for pseudo- $$\omega_{1}$$ -categorical theories of partial orderings, whose connected components form chains. Theories of pseudo- $$\omega_{1}$$ -categorical abelian groups are described, too.

Advanced Topology and Set TheoryRings, Modules, and AlgebrasAdvanced Algebra and Logicmodel theorypartial orderingabelian groups

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