E -combinations of ℵ 0 -categorical linear orderings

  • A. B. Altayeva Al-Farabi Kazakh National University, Institute of Mathematics and Mathematical Modeling of MES RK
  • B. Sh Kulpeshov Kazakh-British Technical University, Institute of Mathematics and Mathematical Modeling of MES RK
  • S. V. Sudoplatov Sudoplatov S.V., Sobolev Institute of Mathematics, Novosibirsk State Technical University


In a series of S.V. Sudoplatov’s works the topological properties of families of theories arestudied. He introduced the concepts of the P-operator and the E-operator, allowing to studythe connections between theories regarding suitable closure operators. These operators make itpossible to generate new theories by means of the considered families of theories, and also find insome cases minimal or smallest generating sets. This research was continued in collaborative workof B.Sh. Kulpeshov and S.V. Sudoplatov for families of ordered theories, including families ofquite o-minimal theories. This article explores the E-combinations of countably many countablycategorical linearly ordered structures of pure linear order. Criterion for countable categoricityof E-combination of countably many copies of an arbitrary countably categorical linear order isobtained. As a consequence, a description of the countable spectrum of such a combination isobtained.


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How to Cite
ALTAYEVA, A. B.; KULPESHOV, B. Sh; SUDOPLATOV, S. V.. E -combinations of ℵ 0 -categorical linear orderings. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 103, n. 3, p. 3-12, oct. 2019. ISSN 2617-4871. Available at: <https://bm.kaznu.kz/index.php/kaznu/article/view/655>. Date accessed: 22 oct. 2020. doi: https://doi.org/10.26577/JMMCS-2019-3-21.
Keywords Е-combination, ordered theory, linearly ordered structure, countable categoricity, countable spectrum