E -комбинации ℵ 0 -категоричных линейных порядков
DOI:
https://doi.org/10.26577/JMMCS-2019-3-21Ключевые слова:
Е-комбинация, упорядоченная теория, линейно упорядоченная структура, счетная категоричность, счетный спектрАннотация
В серии работ Судоплатова С.В. изучались топологические свойства семейств теорий.
Им были введены понятия Р-оператора и Е-оператора, позволяющие изучать связи
между теориями относительно подходящих операторов замыкания. Эти операторы дают
возможность порождать новые теории посредством рассматриваемых семейств теорий,
а также находить в некоторых случаях минимальные или наименьшие порождающие
множества. Данное исследование было продолжено в совместных работах Кулпешова Б.Ш.
и Судоплатова С.В. для семейств упорядоченных теорий, в том числе и для семейств вполне
о-минимальных теорий. В настоящей статье исследуются E-комбинации счетного числа
счетно категоричных линейно упорядоченных структур чистого линейного порядка. Найден
критерий счетной категоричности E-комбинации счетного числа копий произвольного счетно
категоричного линейного порядка. В качестве следствия получено описание счетного спектра
такой комбинации.
Библиографические ссылки
[1] Sudoplatov S.V., ”Combinations of structures”, The Bulletin of Irkutsk State University. Series “Mathematics”, vol. 24 2018): 82-101.
[2] Sudoplatov S.V., ”Closures and generating sets related to combinations of structures”, The Bulletin of Irkutsk State niversity. Series “Mathematics”, vol. 16 (2016): 131-144.
[3] Sudoplatov S.V., ”Families of language uniform theories and their generating sets”, The Bulletin of Irkutsk State University. Series “Mathematics”, vol. 17 (2016): 62-76.
[4] Sudoplatov S.V., ”On semilattices and lattices for families of theories”, Siberian Electronic Mathematical Reports, vol. 14 (2017): 980-985.
[5] Sudoplatov S.V., ”Combinations related to classes of finite and countably categorical structures and their theories”, Siberian Electronic Mathematical Reports, vol. 14 (2017): 135-150.
[6] Sudoplatov S.V., ”Relative e-spectra, relative closures, and semilattices for families of theories”, Siberian Electronic Mathematical Reports, vol. 14 (2017): 296-307.
[7] Pavlyuk In.I., Sudoplatov S.V., ”Families of theories of Ab elian groups and their closures”, Bulletin of Karaganda University. Mathematics, vol. 92, No. 4 (2018): 72-78.
[8] Kulp eshov B.Sh., Sudoplatov S.V., ”On P-combinations of ordered theories”, Traditional International April Mathematical Conference (abstracts), Institute of Mathematics and Mathematical Modeling, Almaty (2019): 30-31.
[9] Kulpeshov B.Sh., Sudoplatov S.V., ”On Ehrehfeuchtness of a P-combination of irdered theories”, Materials of the International Conference ”Algebra and Mathematical Logic: theory and applications”, Kazan: Kazan Federal University (2019): 131-133.
[10] Kulpeshov B.Sh., Sudoplatov S.V., ”P-combination of ordered structures”, Abstracts of the International Conference ”Maltsev Meeting”, Novosibirsk: Sobolev Institute of Mathematics (2019): 190.
[11] Rosenstein J.G., ” ℵ 0-categoricity of linear orderings”, Fundamenta Mathematicae, vol. 64 (1969): 1-5.
[12] Feferman S., Vaught R., ”The first order properties of products of algebraic systems”, Fundamenta Mathematicae, vol. 47 1959): 57-103.
[13] Kulpeshov B.Sh., ”Convexity rank and orthogonality in weakly o-minimal theories”, News of National Academy of Sciences of the Republic of Kazakhstan, series physics-mathematics, vol. 227 (2003): 26-31.
[14] Kulpeshov B.Sh., Sudoplatov S.V., ”Vaught’s conjecture for quite o-minimal theories”, Annals of Pure and Applied Logic, vol. 168 (2017): 129-149.
[15] Kulpeshov B.Sh., ”Countably categorical quite o-minimal theories”, Journal of Mathematical Sciences, vol. 188 (2013): 387-397.
[16] Rubin M., ”Theories of linear order”, Israel Journal of Mathematics, vol. 17 (1974): 392-443.
[17] Sudoplatov S.V., ”Classification of countable models of complete theories”, Part 1, Novosibirsk: Novosibirsk State Technical University Publishing House (2018): 376 c.
[18] Kulpeshov B.Sh., Sudoplatov S.V., ”Linearly ordered theories which are nearly countably categorical”, Mathematical Notes, vol. 101 (2017): 475-483.
[19] Kulpeshov B.Sh., ”Weakly o-minimal structures and some of their properties”, The Journal of Symbolic Logic, vol. 63 (1998): 1511-1528.
[20] Mayer L.L., ”Vaught’s conjecture for o-minimal theories”, The Journal of Symbolic Logic, vol. 53 (1988): 146-159.
[2] Sudoplatov S.V., ”Closures and generating sets related to combinations of structures”, The Bulletin of Irkutsk State niversity. Series “Mathematics”, vol. 16 (2016): 131-144.
[3] Sudoplatov S.V., ”Families of language uniform theories and their generating sets”, The Bulletin of Irkutsk State University. Series “Mathematics”, vol. 17 (2016): 62-76.
[4] Sudoplatov S.V., ”On semilattices and lattices for families of theories”, Siberian Electronic Mathematical Reports, vol. 14 (2017): 980-985.
[5] Sudoplatov S.V., ”Combinations related to classes of finite and countably categorical structures and their theories”, Siberian Electronic Mathematical Reports, vol. 14 (2017): 135-150.
[6] Sudoplatov S.V., ”Relative e-spectra, relative closures, and semilattices for families of theories”, Siberian Electronic Mathematical Reports, vol. 14 (2017): 296-307.
[7] Pavlyuk In.I., Sudoplatov S.V., ”Families of theories of Ab elian groups and their closures”, Bulletin of Karaganda University. Mathematics, vol. 92, No. 4 (2018): 72-78.
[8] Kulp eshov B.Sh., Sudoplatov S.V., ”On P-combinations of ordered theories”, Traditional International April Mathematical Conference (abstracts), Institute of Mathematics and Mathematical Modeling, Almaty (2019): 30-31.
[9] Kulpeshov B.Sh., Sudoplatov S.V., ”On Ehrehfeuchtness of a P-combination of irdered theories”, Materials of the International Conference ”Algebra and Mathematical Logic: theory and applications”, Kazan: Kazan Federal University (2019): 131-133.
[10] Kulpeshov B.Sh., Sudoplatov S.V., ”P-combination of ordered structures”, Abstracts of the International Conference ”Maltsev Meeting”, Novosibirsk: Sobolev Institute of Mathematics (2019): 190.
[11] Rosenstein J.G., ” ℵ 0-categoricity of linear orderings”, Fundamenta Mathematicae, vol. 64 (1969): 1-5.
[12] Feferman S., Vaught R., ”The first order properties of products of algebraic systems”, Fundamenta Mathematicae, vol. 47 1959): 57-103.
[13] Kulpeshov B.Sh., ”Convexity rank and orthogonality in weakly o-minimal theories”, News of National Academy of Sciences of the Republic of Kazakhstan, series physics-mathematics, vol. 227 (2003): 26-31.
[14] Kulpeshov B.Sh., Sudoplatov S.V., ”Vaught’s conjecture for quite o-minimal theories”, Annals of Pure and Applied Logic, vol. 168 (2017): 129-149.
[15] Kulpeshov B.Sh., ”Countably categorical quite o-minimal theories”, Journal of Mathematical Sciences, vol. 188 (2013): 387-397.
[16] Rubin M., ”Theories of linear order”, Israel Journal of Mathematics, vol. 17 (1974): 392-443.
[17] Sudoplatov S.V., ”Classification of countable models of complete theories”, Part 1, Novosibirsk: Novosibirsk State Technical University Publishing House (2018): 376 c.
[18] Kulpeshov B.Sh., Sudoplatov S.V., ”Linearly ordered theories which are nearly countably categorical”, Mathematical Notes, vol. 101 (2017): 475-483.
[19] Kulpeshov B.Sh., ”Weakly o-minimal structures and some of their properties”, The Journal of Symbolic Logic, vol. 63 (1998): 1511-1528.
[20] Mayer L.L., ”Vaught’s conjecture for o-minimal theories”, The Journal of Symbolic Logic, vol. 53 (1988): 146-159.
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Как цитировать
Altayeva, A. B., Kulpeshov, B. S., & Sudoplatov, S. V. (2019). E -комбинации ℵ 0 -категоричных линейных порядков. Вестник КазНУ. Серия математика, механика, информатика, 103(3), 3–12. https://doi.org/10.26577/JMMCS-2019-3-21
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