Binarity of Almost ω-Categorical Quite o-Minimal Theories

Abstract

Studying the properties of almost ω-categorical quite o-minimal theories, we prove that the arbitrary families of pairwise weakly orthogonal nonalgebraic 1-types in these theories are orthogonal. We also establish the binarity of these theories.

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Correspondence to A. B. Altayeva or B. Sh. Kulpeshov.

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To Academician Yu. L. Ershov’s 80th jubilee.

The authors were partially supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grant AP05132546).

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 484–498.

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Altayeva, A.B., Kulpeshov, B.S. Binarity of Almost ω-Categorical Quite o-Minimal Theories. Sib Math J 61, 379–390 (2020). https://doi.org/10.1134/S0037446620030015

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Keywords

  • almost ω-categoricity
  • weak o-minimality
  • quite o-minimality
  • binary theory