BINARY CONVEXITY RANK IN ALMOST OMEGA-CATEGORICAL WEAKLY O-MINIMAL THEORIES
https://doi.org/10.55452/1998-6688-2022-19-1-23-29
Abstract
The present paper concerns the notion of weak o-minimality that was initially deeply studied by D. Macpherson, D. Marker and C. Steinhorn. A subset A of a linearly ordered structure M is convex if for all a, b Î A and c Î M whenever a < c < b we have c Î A. A weakly o-minimal structure is a linearly ordered structure M = áM, =, <, …ñ such that any definable (with parameters) subset of M is a union of finitely many convex sets in M. A criterion for equality of the binary convexity ranks for non-weakly orthogonal non-algebraic 1-types in almost omega-categorical weakly o-minimal theories in case of existing an element of the set of realizations of one of these types the definable closure of which has a non-empty intersection with the set of realizations of another type is found.
About the Authors
Gaukhar Samatkyzy Amirbek
Kazakh-British Technical University
Kazakhstan
Kazakhstan
Master Student, School of Mathematics and Cybernetics
Beibut Shaiykovich Kulpeshov
Kazakh-British Technical University
Kazakhstan
Kazakhstan
Doctor of Physical and Mathematical Sciences, Professor, School of Mathematics and Cybernetics
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Review
For citations:
Amirbek G.S., Kulpeshov B.Sh. BINARY CONVEXITY RANK IN ALMOST OMEGA-CATEGORICAL WEAKLY O-MINIMAL THEORIES. Herald of the Kazakh-British technical university. 2022;19(1):23-29. https://doi.org/10.55452/1998-6688-2022-19-1-23-29
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