On One Laura Mayer’s Theorem
Baizhanov B. Tazabekova N. Zambarnaya T.
October 2025Multidisciplinary Digital Publishing Institute (MDPI)
Symmetry
2025#17Issue 10
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.
almost orthogonality , convex closure , linear order , monotonicity , number of countable models , small theory , weak convex orthogonality , weak orthogonality , weakly o-minimal theory
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Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
School of Applied Mathematics, Kazakh-British Technical University, Almaty, 050000, Kazakhstan
Faculty of Engineering and Natural Sciences, Department of Mathematics, SDU University, Kaskelen, 040900, Kazakhstan
Institute of Mathematics and Mathematical Modeling
School of Applied Mathematics
Faculty of Engineering and Natural Sciences
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