kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2021-18-4-26-31kaz29-364Research ArticleФИЗИКО-МАТЕМАТИЧЕСКИЕ И ТЕХНИЧЕСКИЕ НАУКИPHYSICAL, MATHEMATICAL AND TECHNICAL SCIENCESОБ 1-НЕРАЗЛИЧИМОСТИ Е-КОМБИНАЦИЙ УПОРЯДОЧЕННЫХ ТЕОРИЙON 1-INDISCERNIBILITY OF E-COMBINATIONS OF ORDERED THEORIEShttps://orcid.org/0000-0002-3268-9389СудоплатовС. В.SudoplatovS. V.

630073, пр. К. Маркса, 20, Новосибирск

Sudoplatov Sergey Vladimirovich, Doctor of Physical and Mathematical Sciences, Leading Researcher, Sobolev Institute of Mathematics; Head of Algebra and Mathematical Logic Department

20, K.Marx avenue, Novosibirsk, 630073

sudoplat@math.nsc.ruНовосибирский государственный технический университетРоссияNovosibirsk State Technical UniversityRussian Federation2021241220211842631Copyright © Судоплатов С.В., 20212021Судоплатов С.В.Sudoplatov S.V.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/364

В настоящей работе мы исследуем свойства, которые сохраняются или приобретаются при комбинировании произвольного числа теорий или структур. В последнее время интерес был проявлен к изучению Р-комбинаций (когда каждая структура выделяется отдельным унарным предикатом) и Е-комбинаций (когда каждая структура выделяется отдельным классом эквивалентности по отношению Е). Здесь мы изучали свойства Е-комбинаций линейно упорядоченных теорий. Установлены 1-неразличимость и плотность слабо о-минимальной Е-комбинации счетного числа копий почти омега-категоричной слабо о-минимальной теории в языке, не содержащем выделенных констант.

In this paper, we investigate properties that are preserved or acquired when combining an arbitrary number of theories or structures. Recently, an interest has been shown in the study of P-combinations (when each structure is distinguished by a separate unary predicate) and E-combinations (when each structure is distinguished by a separate class of equivalence with respect to E). Here we studied the properties of E-combinations of linearly ordered theories. The 1-indiscernibilty and density of a weakly o-minimal E-combination of countably many copies of an almost omega-categorical weakly o-minimal theory in a language that does not contain distinguished constants are established.

линейно упорядоченная структураслабая о-минимальностьЕ-комбинацияомега-категоричностьплотный порядокlinearly ordered structureweak o-minimalityE-combinationomega-categoricitydense orderingThe research has been supported by Program of fundamental researches of Siberian Branch of Russian Academy of sciences No. I.1.1, project No. № 0314-2019-0002, and by Science Committee of Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08855544).ReferencesSudoplatov S.V. Combinations of structures // The Bulletin of Irkutsk State University. Series “Mathematics”. – 2018. – Vol. 24. – pp. 82–101.Sudoplatov S.V. Combinations of structures // The Bulletin of Irkutsk State University. Series “Mathematics”. – 2018. – Vol. 24. – pp. 82–101.Sudoplatov S.V. Closures and generating sets related to combinations of structures // The Bulletin of Irkutsk State University. Series “Mathematics”. – 2016. – Vol. 16. – pp. 131–144.Sudoplatov S.V. Closures and generating sets related to combinations of structures // The Bulletin of Irkutsk State University. Series “Mathematics”. – 2016. – Vol. 16. – pp. 131–144.Sudoplatov S.V. Families of language uniform theories and their generating sets // The Bulletin of Irkutsk State University. Series “Mathematics”. – 2016. – Vol. 17. – pp. 62–76.Sudoplatov S.V. Families of language uniform theories and their generating sets // The Bulletin of Irkutsk State University. Series “Mathematics”. – 2016. – Vol. 17. – pp. 62–76.Sudoplatov S.V. On semilattices and lattices for families of theories // Siberian Electronic Mathematical Reports. – 2017. – Vol. 14. – pp. 980–985.Sudoplatov S.V. On semilattices and lattices for families of theories // Siberian Electronic Mathematical Reports. – 2017. – Vol. 14. – pp. 980–985.Sudoplatov S.V. Combinations related to classes of finite and countably categorical structures and their theories // Siberian Electronic Mathematical Reports. – 2017. – Vol. 14. – pp. 135–150.Sudoplatov S.V. Combinations related to classes of finite and countably categorical structures and their theories // Siberian Electronic Mathematical Reports. – 2017. – Vol. 14. – pp. 135–150.Sudoplatov S.V. Relative -spectra, relative closures, and semilattices for families of theories // Siberian Electronic Mathematical Reports. – 2017. – Vol. 14. – pp. 296–307.Sudoplatov S.V. Relative -spectra, relative closures, and semilattices for families of theories // Siberian Electronic Mathematical Reports. – 2017. – Vol. 14. – pp. 296–307.Pavlyuk In.I., Sudoplatov S.V. Families of theories of Abelian groups and their closures // Bulletin of Karaganda University. Mathematics. – 2018. – Vol. 92, No. 4. – pp. 72–78.Pavlyuk In.I., Sudoplatov S.V. Families of theories of Abelian groups and their closures // Bulletin of Karaganda University. Mathematics. – 2018. – Vol. 92, No. 4. – pp. 72–78.Kulpeshov B.Sh., Sudoplatov S.V., On -combinations of ordered theories // Traditional International April Mathematical Conference, (Institute of Mathematics and Mathematical Modeling, Almaty, 5-8 April 2019), pp. 30–31.Kulpeshov B.Sh., Sudoplatov S.V., On -combinations of ordered theories // Traditional International April Mathematical Conference, (Institute of Mathematics and Mathematical Modeling, Almaty, 5-8 April 2019), pp. 30–31.Kulpeshov B.Sh., Sudoplatov S.V., On Ehrenfeuchtness of a -combination of ordered theories // Materials of the International Conference “Algebra and Mathematical Logic: theory and applications” (Kazan, Kazan Federal University, 24-28 June 2019), pp. 131–133.Kulpeshov B.Sh., Sudoplatov S.V., On Ehrenfeuchtness of a -combination of ordered theories // Materials of the International Conference “Algebra and Mathematical Logic: theory and applications” (Kazan, Kazan Federal University, 24-28 June 2019), pp. 131–133.Kulpeshov B.Sh., Sudoplatov S.V., -combinations of ordered structures // International Conference “Mal’tsev Meeting” (Novosibirsk, Sobolev Institute of Mathematics, 18-24 August 2019), P. 190.Kulpeshov B.Sh., Sudoplatov S.V., -combinations of ordered structures // International Conference “Mal’tsev Meeting” (Novosibirsk, Sobolev Institute of Mathematics, 18-24 August 2019), P. 190.Kulpeshov B.Sh., Sudoplatov S.V. -combinations of ordered theories // Lobachevskii Journal of Mathematics. – 2020. – Vol. 41, No. 2. – pp. 227–237.Kulpeshov B.Sh., Sudoplatov S.V. -combinations of ordered theories // Lobachevskii Journal of Mathematics. – 2020. – Vol. 41, No. 2. – pp. 227–237.Kulpeshov B.Sh., Sudoplatov S.V. -combinations of almost -categorical weakly o-minimal theories // Lobachevskii Journal of Mathematics. – 2021. – Vol. 42, No. 4. – pp. 743–750.Kulpeshov B.Sh., Sudoplatov S.V. -combinations of almost -categorical weakly o-minimal theories // Lobachevskii Journal of Mathematics. – 2021. – Vol. 42, No. 4. – pp. 743–750.Macpherson H. D., Marker D., and Steinhorn C. Weakly o-minimal structures and real closed fields // Transactions of The American Mathematical Society. – 2000. – Vol. 352, No. 12. – pp. 5435– 5483.Macpherson H. D., Marker D., and Steinhorn C. Weakly o-minimal structures and real closed fields // Transactions of The American Mathematical Society. – 2000. – Vol. 352, No. 12. – pp. 5435– 5483.Ikeda K., Pillay A., Tsuboi A. On theories having three countable models, Mathematical Logic Quarterly. – 1998. – Vol. 44, No. 2. – pp. 161–166.Ikeda K., Pillay A., Tsuboi A. On theories having three countable models, Mathematical Logic Quarterly. – 1998. – Vol. 44, No. 2. – pp. 161–166.Sudoplatov S.V. Classification of countable models of complete theories. – Part 1. – Novosibirsk: Novosibirsk State Technical University Publishing House. – 2018. – ISBN 978-5-7782- 3527-4. – P. 326.Sudoplatov S.V. Classification of countable models of complete theories. – Part 1. – Novosibirsk: Novosibirsk State Technical University Publishing House. – 2018. – ISBN 978-5-7782- 3527-4. – P. 326.Baizhanov B.S. Expansion of a model of a weakly o-minimal theory by a family of unary predicates // The Journal of Symbolic Logic. – 2001. – Vol. 66. – pp. 1382–1414.Baizhanov B.S. Expansion of a model of a weakly o-minimal theory by a family of unary predicates // The Journal of Symbolic Logic. – 2001. – Vol. 66. – pp. 1382–1414.Kulpeshov B.Sh., Sudoplatov S.V. Linearly ordered theories which are nearly countably categorical // Mathematical Notes. – 2017. – Vol. 101, No. 3. – pp. 475–483.Kulpeshov B.Sh., Sudoplatov S.V. Linearly ordered theories which are nearly countably categorical // Mathematical Notes. – 2017. – Vol. 101, No. 3. – pp. 475–483.

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