Submission date: 10 August 2022

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.

Mathematics Subject Classification: 06A75, 03C10, 03C15, 03C50

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Full text arXiv 2208.05097: pdf, ps.