Abstract
Continuing the study of weak \( o \)-minimality, we prove a theorem on the behavior of a definable unary function on the set of realizations of a nonalgebraic 1-type in an arbitrary weakly \( o \)-minimal theory. Under study are the properties of almost \( \omega \)-categorical weakly \( o \)-minimal theories. We find sufficient conditions both for weak orthogonality and orthogonality of any finite family of nonalgebraic 1-types over the empty set. The main result of the paper is a criterion for binarity of almost \( \omega \)-categorical weakly \( o \)-minimal theories.
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Funding
This research has been funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08855544).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 6, pp. 1313–1329. https://doi.org/10.33048/smzh.2021.62.608
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Kulpeshov, B.S. A Criterion for Binarity of Almost \( \omega \)-Categorical Weakly \( o \)-Minimal Theories. Sib Math J 62, 1063–1075 (2021). https://doi.org/10.1134/S0037446621060082
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DOI: https://doi.org/10.1134/S0037446621060082