Abstract:
For families of all theories of arbitrary given languages we describe ranks and degrees. In particular, we characterize (non-)totally transcendental families. We apply these characterizations for the families of all theories of given languages, with models of given finite or infinite cardinality.
Keywords and phrases:
family of theories, rank, degree.
This research was partially supported by the Committee of Science of the Ministry of the Education and Science of the Republic of Kazakhstan (Grants No. AP08855497) and the Programme of
fundamental scientific research of the SB RAS No. I.1.1, project No. 0314-2019-0002 and Russian
Foundation for Basic Researches (Grant No. 20-31-90003).
\Bibitem{MarSud21}
\by N.~D.~Markhabatov, S.~V.~Sudoplatov
\paper Ranks for families of all theories of given languages
\jour Eurasian Math. J.
\yr 2021
\vol 12
\issue 2
\pages 52--58
\mathnet{http://mi.mathnet.ru/emj403}
\crossref{https://doi.org/10.32523/2077-9879-2021-12-2-52-58}
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Linking options:
https://www.mathnet.ru/eng/emj403
https://www.mathnet.ru/eng/emj/v12/i2/p52
This publication is cited in the following 9 articles:
B. Sh. Kulpeshov, In. I. Pavlyuk, S. V. Sudoplatov, “Ranks and approximations for families of order theories”, Math. Notes, 116:4 (2024), 669–684
Beibut Sh. Kulpeshov, Sergey V. Sudoplatov, “Ranks, spectra and their dynamics for families of constant expansions of theories”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 45 (2023), 121–137
N. D. Markhabatov, “APPROXIMATIONS OF THE THEORIES OF STRUCTURES WITH ONE EQUIVALENCE RELATION”, jour, 20:2 (2023), 67
I. V. Latkin, “The recognition complexity of decidable theories”, Eurasian Math. J., 13:1 (2022), 44–68
B. Sh. Kulpeshov, S. V. Sudoplatov, “Properties of ranks for families of strongly minimal theories”, Sib. elektron. matem. izv., 19:1 (2022), 120–124
S. V. Sudoplatov, “Special relations for formulae, their equivalence relations and theories”, Sib. elektron. matem. izv., 19:1 (2022), 259–272
Sergey V. Sudoplatov, “Topologies and ranks for families of theories in various languages”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 40 (2022), 78–92
N. D. Markhabatov, S. V. Sudoplatov, “Ranks for families of regular graph theories”, jour, 19:3 (2022), 54
N. D. Markhabatov, “Model-theoretic and topological properties of families of theories”, Algebra and Logic, 60:3 (2021), 232–235
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