kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2022-19-2-20-28kaz29-520Research ArticleФИЗИКО-МАТЕМАТИЧЕСКИЕ И ТЕХНИЧЕСКИЕ НАУКИPHYSICAL, MATHEMATICAL AND TECHNICAL SCIENCESО (p, q)-СЕКАТОРАХ В ПОЧТИ ОМЕГА-КАТЕГОРИЧНЫХ СЛАБО О-МИНИМАЛЬНЫХ ТЕОРИЯХON (p, q)-SPLITTING FORMULAS IN ALMOST OMEGA-CATEGORICAL WEAKLY O-MINIMAL THEORIEShttps://orcid.org/0000-0001-7042-8705ИЗБАСАРОВА. А.IZBASAROVA. A.

Избасаров Азамат Абилкаирович - магистрант, факультет математики и кибернетики

050000, г. Алматы, ул. Толе би, 59

Izbassarov Azamat Abilkairovich - Master Student, School of Mathematics and Cybernetics

050000, Almaty, Tole bi street, 59

az_izbasarov@kbtu.kzhttps://orcid.org/0000-0002-4242-0463КУЛПЕШОВБ. Ш.KULPESHOVB. S.

Кулпешов Бейбут Шайыкович - доктор физико-математических наук, профессор, факультет математики и кибернетики

050000, г. Алматы, ул. Толе би, 59

Kulpeshov Beibut Shaiykovich - Doctor of Physical and Mathematical Sciences, Professor, School of Mathematics and Cybernetics

050000, Almaty, Tole bi street, 59

b.kulpeshov@kbtu.kzhttps://orcid.org/0000-0003-4005-6060ЕМЕЛЬЯНОВД. Ю.EMELYANOVD. Y.

Емельянов Дмитрий Юрьевич - ассистент

630073, г. Новосибирск, пр. К. Маркса, 20

Emelyanov Dmitry Yurevich - Assistant

630073, Novosibirsk, K. Marx ave., 20

dima-pavlyk@mail.ruКазахстанско-Британский технический университетКазахстанKazakh-British Technical UniversityKazakhstanНовосибирский государственный технический университетРоссияNovosibirsk State Technical UniversityRussian Federation2022040720221922028Copyright © ИЗБАСАРОВ А.А., КУЛПЕШОВ Б.Ш., ЕМЕЛЬЯНОВ Д.Ю., 20222022ИЗБАСАРОВ А.А., КУЛПЕШОВ Б.Ш., ЕМЕЛЬЯНОВ Д.Ю.IZBASAROV A.A., KULPESHOV B.S., EMELYANOV D.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/520

Настоящая статья касается понятия слабой о-минимальности, введенного М. Дикманном и первоначально исследованного Д. Макферсоном, Д. Маркером и Ч. Стейнхорном. Слабая о-минимальность является обобщением понятия о-минимальности, введенного А. Пиллэем и Ч. Стейнхорном в серии совместных статей. Как известно, упорядоченное поле вещественных чисел является примером о-минимальной структуры. Мы продолжаем изучение свойств почти омега-категоричных слабо о-минимальных теорий. Почти омега-категоричность – это понятие, обобщающее понятие омега-категоричности. Недавно был получен критерий бинарности почти омега-категоричных слабо о-минимальных теорий в терминах ранга выпуклости. Бинарный ранг выпуклости – это ранг выпуклости, в котором параметрически определимые отношения эквивалентности заменяются пусто-определимыми отношениями эквивалентности. (p, q)-секаторы выражают связь между не слабо ортогональными неалгебраическими 1-типами в слабо о-минимальных теориях. В большинстве случаев бинарные ранги выпуклости не слабо ортогональных не- алгебраических 1-типов не совпадают. Основным результатом данной статьи является нахождение необходимых и достаточных условий равенства бинарных рангов выпуклости для не слабо ортогональных неалгебраических 1-типов в почти омега-категоричных слабо о-минимальных теориях в терминах (p, q)-секаторов.

The present paper concerns the notion of weak o-minimality introduced by M. Dickmann and originally studied by D. Macpherson, D. Marker, and C. Steinhorn. Weak o-minimality is a generalization of the notion of o-minimality introduced by A. Pillay and C. Steinhorn in series of joint papers. As is known, the ordered field of real numbers is an example of an o-minimal structure. We continue studying properties of almost omega-categorical weakly o-minimal theories. Almost omega-categoricity is a notion generalizing the notion of omega-categoricity. Recently, a criterion for binarity of almost omega-categorical weakly o-minimal theories in terms of convexity rank has been obtained. Binary convexity rank is the convexity rank in which parametrically definable equivalence relations are replaced by ∅ - definable equivalence relations. (p, q)-splitting formulas express a connection between non-weakly orthogonal non-algebraic 1-types in weakly o-minimal theories. In many cases, the binary convexity ranks of non-weakly orthogonal non-algebraic 1-types are not equal. The main result of this paper is finding necessary and sufficient conditions for equality of the binary convexity ranks for non-weakly orthogonal non-algebraic 1-types in almost omega-categorical weakly o-minimal theories in terms of (p, q)-splitting formulas.

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The authors declare that there are no conflicts of interest present.