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Article · Sibirskie Elektronnye Matematicheskie Izvestiya · December 31, 2023

Spherical orders, properties and countable spectra of their theories

B. Sh. Kulpeshov, Sergey Vladimirovich Sudoplatov

Beibut Kulpeshov
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Abstract

We study semantic and syntactic properties of spherical orders and their elementary theories, including nite 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 conrmed for countable constant expansions of dense n-spherical theories.

Advanced Topology and Set TheoryRings, Modules, and AlgebrasAdvanced Algebra and Logicfinite orderelementary theorydecidability

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