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Matematicheskie Zametki, 2024, Volume 116, Issue 4, Pages 531–551
DOI: https://doi.org/10.4213/mzm14207 (Mi mzm14207) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Ranks and approximations for families of order theories

B. Sh. Kulpeshovab, In. I. Pavlyukc, S. V. Sudoplatovcd

a Kazakh-British Technical University
b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty
c Novosibirsk State Technical University
d Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (666 kB) First page Citations (2)
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DOI: https://doi.org/10.4213/mzm14207
Abstract: Rank values for various families of order theories are described as depending on the languages under consideration; a description of ee-total transcendence in terms of these languages is also given. Approximations of order theories are studied, including approximations by finite and countably categorical orders. Closures are studied and ranks are described for families of order theories, including the families of o-minimal and weakly o-minimal theories of various signatures, as well as theories of pure linear orders with various constraints on the discrete parts.
Keywords: rank, approximation, family of theories, ordered theory.
Funding agency Grant number
Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan AP19674850
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0012
This work was financially supported by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (grant no. AP19674850) and was carried out in the framework of the state assignment to Sobolev Institute of Mathematics (grant no. FWNF-2022-0012).
Received: 30.11.2023
Revised: 10.05.2024
English version:
Mathematical Notes, 2024, Volume 116, Issue 4, Pages 669–684
DOI: https://doi.org/10.1134/S0001434624090256
Bibliographic databases:
Document Type: Article
UDC: 510.67
MSC: 03C64, 03C52, 03C68
Language: Russian
Citation: B. Sh. Kulpeshov, In. I. Pavlyuk, S. V. Sudoplatov, “Ranks and approximations for families of order theories”, Mat. Zametki, 116:4 (2024), 531–551; Math. Notes, 116:4 (2024), 669–684
Citation in format AMSBIB
\Bibitem{KulPavSud24}
\by B.~Sh.~Kulpeshov, In.~I.~Pavlyuk, S.~V.~Sudoplatov
\paper Ranks and approximations for families of order theories
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 4
\pages 531--551
\mathnet{http://mi.mathnet.ru/mzm14207}
\crossref{https://doi.org/10.4213/mzm14207}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 4
\pages 669--684
\crossref{https://doi.org/10.1134/S0001434624090256}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85213364325}
Linking options:
  • https://www.mathnet.ru/eng/mzm14207
  • https://doi.org/10.4213/mzm14207
  • https://www.mathnet.ru/eng/mzm/v116/i4/p531
    • This publication is cited in the following 2 articles:
    1. B. Sh. Kulpeshov, In. I. Pavlyuk, S. V. Sudoplatov, “Psevdo-schetno-kategorichnye formuly i teorii”, Matem. zametki, 117:3 (2025), 422–442  mathnet  crossref
    2. B. Sh. Kulpeshov, In. I. Pavlyuk, S. V. Sudoplatov, “Pseudo-strongly-minimal Structures and Theories”, Lobachevskii J Math, 45:12 (2024), 6515  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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