A Criterion for Binarity of Almost ω-Categorical Weakly o-Minimal Theories

Kulpeshov B.S.
November 2021 Pleiades journals

Siberian Mathematical Journal
2021 #62 Issue 6 1063 - 1075 pp.

Continuing the study of weak o-minimality, we prove a theorem on the behaviorof a definable unary function on the set of realizations of a nonalgebraic 1-typein an arbitrary weakly o-minimal theory. Under study are the properties of almost ω-categoricalweakly o-minimal theories. We find sufficient conditions bothfor weak orthogonality and orthogonality of any finite family of nonalgebraic1-types over the empty set.The main result of the paper is a criterion for binarity of almost ω-categorical weakly o-minimal theories.

510.67 , almost ω-categoricity , binary theory , convexity rank , weak o-minimality

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Kazakh–British Technical University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Novosibirsk State Technical University, Novosibirsk, Russian Federation

Kazakh–British Technical University
Institute of Mathematics and Mathematical Modeling
Novosibirsk State Technical University

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