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Mathematics
Volume 13
Issue 20
10.3390/math13203271
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Orthogonality of 1-Types over Sets, Neighborhoods of Sets in 1-Types in Weakly Ordered Minimal Theories

by
Bektur Baizhanov
1,2,
Nargiza Tazabekova
1,2,3,* and
Tatyana Zambarnaya
1
1
Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan
2
School of Applied Mathematics, Kazakh-British Technical University, Almaty 050000, Kazakhstan
3
Faculty of Engineering and Natural Sciences, Department of Mathematics, SDU University, Kaskelen 040900, Kazakhstan
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(20), 3271; https://doi.org/10.3390/math13203271 (registering DOI)
Submission received: 26 August 2025 / Revised: 7 October 2025 / Accepted: 10 October 2025 / Published: 13 October 2025
(This article belongs to the Section A: Algebra and Logic)
Versions Notes

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 deeper understanding of the geometry of types in weakly ordered minimal theories and provides tools that may be applied in related model-theoretic contexts.
Keywords: weakly o-minimal theories; weak orthogonality; almost orthogonality; convex set; quasisolitary type; quasirational type; irrational type weakly o-minimal theories; weak orthogonality; almost orthogonality; convex set; quasisolitary type; quasirational type; irrational type

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MDPI and ACS Style

Baizhanov, B.; Tazabekova, N.; Zambarnaya, T. Orthogonality of 1-Types over Sets, Neighborhoods of Sets in 1-Types in Weakly Ordered Minimal Theories. Mathematics 2025, 13, 3271. https://doi.org/10.3390/math13203271

AMA Style

Baizhanov B, Tazabekova N, Zambarnaya T. Orthogonality of 1-Types over Sets, Neighborhoods of Sets in 1-Types in Weakly Ordered Minimal Theories. Mathematics. 2025; 13(20):3271. https://doi.org/10.3390/math13203271

Chicago/Turabian Style

Baizhanov, Bektur, Nargiza Tazabekova, and Tatyana Zambarnaya. 2025. "Orthogonality of 1-Types over Sets, Neighborhoods of Sets in 1-Types in Weakly Ordered Minimal Theories" Mathematics 13, no. 20: 3271. https://doi.org/10.3390/math13203271

APA Style

Baizhanov, B., Tazabekova, N., & Zambarnaya, T. (2025). Orthogonality of 1-Types over Sets, Neighborhoods of Sets in 1-Types in Weakly Ordered Minimal Theories. Mathematics, 13(20), 3271. https://doi.org/10.3390/math13203271

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