SPHERICAL ORDERS, PROPERTIES AND COUNTABLE SPECTRA OF THEIR THEORIES
Kulpeshov B.Sh. Sudoplatov S.V.
2023Sobolev Institute of Mathematics
Siberian Electronic Mathematical Reports
2023#20Issue 2588 - 599 pp.
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.
countably categorical theory , dense spherical order , elementary theory , spectrum of countable models , spherical order , Vaught conjecture
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Beibut Shaiykovich Kulpeshov Kazakh British Technical University, Tole bi street, 59, Almaty, 050000, Kazakhstan
Novosibirsk State Technical University, K. Marx avenue, 20, Novosibirsk, 630073, Russian Federation
Insititute of Mathematics and Mathematical Modeling, Shevchenko street, 28, Almaty, 050010, Kazakhstan
Sergey Vladimirovich Sudoplatov Novosibirsk State Technical University, K. Marx avenue, 20, Novosibirsk, 630073, Russian Federation
Sobolev Institute of Mathematics, Academician Koptyug avenue, 4, Novosibirsk, 630090, Russian Federation
Beibut Shaiykovich Kulpeshov Kazakh British Technical University
Novosibirsk State Technical University
Insititute of Mathematics and Mathematical Modeling
Sergey Vladimirovich Sudoplatov Novosibirsk State Technical University
Sobolev Institute of Mathematics
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