Geodesic
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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     author = {B. Sh. Kulpeshov and S. V. Sudoplatov},
     title = {Spherical orders, properties and countable spectra of their theories},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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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/