Abstract
Rank values for various families of ordered theories are described as depending on the languages under consideration; a description of \(\mathrm{e}\)-total transcendence in terms of these languages is also given. Approximations of ordered theories are studied, including approximations by finite and countably categorical orders. Closures are studied and ranks are described for families of ordered theories, including the families of o-minimal and weakly o-minimal theories of various signatures, as well as theories of pure linear orders with various constraints on the discrete parts.
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Acknowledgments
The authors thank the anonymous referees, whose constructive comments and suggestions helped to improve the content of the paper.
Funding
This work was financially supported by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (grant no. AP19674850) and was carried out in the framework of the state assignment to Sobolev Institute of Mathematics (grant no. FWNF-2022-0012).
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Translated from Matematicheskie Zametki, 2024, Vol. 116, No. 4, pp. 531–551 https://doi.org/10.4213/mzm14207.
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Kulpeshov, B.S., Pavlyuk, I.I. & Sudoplatov, S.V. Ranks and Approximations for Families of Ordered Theories. Math Notes 116, 669–684 (2024). https://doi.org/10.1134/S0001434624090256
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DOI: https://doi.org/10.1134/S0001434624090256