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arXiv · 2208.05097

Spherical orders, properties and countable spectra of their theories

Beibut Sh. Kulpeshov·Sergey V. Sudoplatov
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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.

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Beibut Sh. Kulpeshov, Sergey V. Sudoplatov. 2022-08-10. Spherical orders, properties and countable spectra of their theories. https://arxiv.org/abs/2208.05097

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