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Keywords = weakly o-minimal theories

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18 pages, 310 KB  
Article
Orthogonality of 1-Types over Sets, Neighborhoods of Sets in 1-Types in Weakly Ordered Minimal Theories
by Bektur Baizhanov, Nargiza Tazabekova and Tatyana Zambarnaya
Mathematics 2025, 13(20), 3271; https://doi.org/10.3390/math13203271 - 13 Oct 2025
Viewed by 219
Abstract
This paper examines the relationship between weak orthogonality and almost orthogonality for complete non-algebraic 1-types in weakly ordered minimal theories. A central element of our approach is the concept of neighborhoods, which encapsulate local properties of type realizations. This work contributes to a [...] Read more.
This paper examines the relationship between weak orthogonality and almost orthogonality for complete non-algebraic 1-types in weakly ordered minimal theories. A central element of our approach is the concept of neighborhoods, which encapsulate local properties of type realizations. This work contributes to a deeper understanding of the geometry of types in weakly ordered minimal theories and provides tools that may be applied in related model-theoretic contexts. Full article
(This article belongs to the Section A: Algebra and Logic)
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18 pages, 347 KB  
Article
On One Laura Mayer’s Theorem
by Bektur Baizhanov, Nargiza Tazabekova and Tatyana Zambarnaya
Symmetry 2025, 17(10), 1641; https://doi.org/10.3390/sym17101641 - 3 Oct 2025
Viewed by 273
Abstract
The article’s primary focus is on the study of the number of countable non-isomorphic models of linearly ordered theories. The orthogonality of 1-types and their convex closures is employed to analyse a class of theories with a specific type of monotonic non-orthogonality, which [...] Read more.
The article’s primary focus is on the study of the number of countable non-isomorphic models of linearly ordered theories. The orthogonality of 1-types and their convex closures is employed to analyse a class of theories with a specific type of monotonic non-orthogonality, which includes weakly o-minimal theories. For such theories, a theorem analogous to L. Mayer’s result on the independence of any pairwise independent family of 1-types in o-minimal theories is proven. The article provides conditions for the infinity and maximality of the countable spectrum of weakly o-minimal theories. Full article
(This article belongs to the Section Mathematics)
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