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Spherical orders, properties and countable spectra of their theories
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 588-599.

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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. 
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B. Sh. Kulpeshov; S. V. Sudoplatov. Spherical orders, properties and countable spectra of their theories. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 588-599. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a1/

[1] S.V. Sudoplatov, “Arities and aritizabilities of first-order theories”, Sib. Èlectron. Math. Izv., 19:2 (2022), 889–901 | MR

[2] S.V. Sudoplatov, “Almost $n$-ary and almost $n$-aritizable theories”, Sib. Èlectron. Math. Izv., 20:1 (2023), 132–139 | MR

[3] B.Sh. Kulpeshov, H.D. Macpherson, “Minimality conditions on circularly ordered structures”, Math. Log. Q., 51:4 (2005), 377–399 | DOI | MR | Zbl

[4] A.B. Altaeva, B.Sh. Kulpeshov, “On almost binary weakly circularly minimal structures”, Bulletin of Karaganda University, Mathematics, 78:2 (2015), 74–82 | MR

[5] B.Sh. Kulpeshov, “On almost binarity in weakly circularly minimal structures”, Eurasian Math. J., 7:2 (2016), 38–49 | MR | Zbl

[6] A.L. Semenov, “Finiteness conditions for algebras of relations”, Proc. Steklov Inst. Math., 242 (2003), 92–96 | MR | Zbl

[7] S.V. Sudoplatov, Classification of countable models of complete theories, NSTU, Novosibirsk, 2018

[8] E.A. Palyutin, J. Saffe, S.S. Starchenko, “Models of superstable Horn theories”, Algebra Logic, 24:3 (1985), 171–210 | DOI | MR | Zbl

[9] P.S. Modenov, A.S. Parkhomenko, Geometric transformations, Izdat. Mosk. Univ., M., 1961 | MR | Zbl

[10] N.N. Stepanov, Spherical trigonometry, ONTI NKTP USSR, M., 1948 | Zbl

[11] S.V. Sudoplatov, Group polygonometries, NSTU, 2013

[12] Yu.L. Ershov, E.A. Palyutin, Mathematical logic, Nauka, M., 2011 | MR | Zbl

[13] R. Vaught, “Denumerable models of complete theories”, Infinitistic Methods, Proc. Symp. Foundations Math. (Warsaw 1959), Pergamon, London, 1961, 303–321 | MR | Zbl

[14] T.S. Millar, “Decidable Ehrenfeucht theories”, Proc. Sympos. Pure Math., 42 (1985), 311–321 | DOI | MR | Zbl

[15] L.L. Mayer, “Vaught's conjecture for $o$-minimal theories”, J. Symb. Log., 53:1 (1988), 146–159 | DOI | MR | Zbl

[16] A. Pillay, C. Steinhorn, “Definable sets in ordered structures. I”, Trans. Am. Math. Soc., 295:2 (1986), 565–592 | DOI | MR | Zbl

[17] B.Sh. Kulpeshov, S.V. Sudoplatov, “Distributions of countable models of quite $o$-minimal Ehrenfeucht theories”, Eurasian Math. J., 11:3 (2020), 66–78 | DOI | MR | Zbl

[18] S.V. Sudoplatov, “Distributions of countable models of disjoint unions of Ehrenfeucht theories”, Lobachevskii J. Math., 42:1 (2021), 195–205 | DOI | MR | Zbl