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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 588–599
DOI: https://doi.org/10.33048/semi.2023.20.034 (Mi semr1597) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematical logic, algebra and number theory

Spherical orders, properties and countable spectra of their theories

B. Sh. Kulpeshovabc, S. V. Sudoplatovcd

a Insititute of Mathematics and Mathematical Modeling, Shevchenko street, 28, 050010, Almaty, Kazakhstan
b Kazakh British Technical University, Tole bi street, 59, 050000, Almaty, Kazakhstan
c Novosibirsk State Technical University, K. Marx avenue, 20, 630073, Novosibirsk, Russia
d Sobolev Institute of Mathematics, Academician Koptyug avenue, 4, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2023.20.034
Abstract: We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and decidable. The values for spectra of countable models of unary expansions of $n$-spherical theories are described. The Vaught conjecture is confirmed for countable constant expansions of dense $n$-spherical theories.
Keywords: spherical order, elementary theory, dense spherical order, countably categorical theory, spectrum of countable models, Vaught conjecture.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP19674850
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0012
The research is supported by Committee of Science in Science and Higher Education Ministry of the Republic of Kazakhstan, Grant No. AP19674850. The work of the second author was carried out in the framework of the State Contract of the Sobolev Institute of Mathematics, Project No. FWNF-2022-0012.
Received October 11, 2022, published July 21, 2023
Document Type: Article
UDC: 510.67
MSC: 06A75, 03C10, 03C15, 03C50
Language: English
Citation: B. Sh. Kulpeshov, S. V. Sudoplatov, “Spherical orders, properties and countable spectra of their theories”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 588–599
Citation in format AMSBIB
\Bibitem{KulSud23}
\by B.~Sh.~Kulpeshov, S.~V.~Sudoplatov
\paper Spherical orders, properties and countable spectra of their theories
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 588--599
\mathnet{http://mi.mathnet.ru/semr1597}
\crossref{https://doi.org/10.33048/semi.2023.20.034}
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