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

Bektur Baizhanov, Nargiza Tazabekova () and Tatyana Zambarnaya
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Bektur Baizhanov: Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan
Nargiza Tazabekova: Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan
Tatyana Zambarnaya: Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan

Mathematics, 2025, vol. 13, issue 20, 1-18

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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