Algebras of binary formulas for $\aleph_0$-categorical weakly circularly minimal theories: monotonic case Full article
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Вестник Карагандинского университета. Серия Математика (Bulletin of the Karaganda University-Mathematics)
ISSN: 2518-7929 , E-ISSN: 2663-5011 |
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| Output data | Year: 2024, Volume: 113, Number: 1, Pages: 112-127 Pages count : 16 DOI: 10.31489/2024M1/112-127 | ||||||||
| Tags | circularly ordered structure, binary formula, isolating formula, algebra of formulas, 0-categorical theory, weak circular minimality, convexity rank, automorphism group, transitivity, primitiveness, mdeterministicity. | ||||||||
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0012 |
Abstract:
This article concerns the notion of weak circular minimality being a variant of o-minimality for circularly ordered structures. Algebras of binary isolating formulas are studied for countably categorical weakly circularly minimal theories of convexity rank greater than 1 having both a 1-transitive non-primitive automorphism group and a non-trivial strictly monotonic function acting on the universe of a structure. On the basis of the study, the authors present a description of these algebras. It is shown that there exist both commutative and non-commutative algebras among these ones. A strict m-deterministicity of such algebras for some natural number m is also established.
Cite:
Kulpeshov B.S.
, Sudoplatov S.V.
Algebras of binary formulas for $\aleph_0$-categorical weakly circularly minimal theories: monotonic case
Вестник Карагандинского университета. Серия Математика (Bulletin of the Karaganda University-Mathematics). 2024. V.113. N1. P.112-127. DOI: 10.31489/2024M1/112-127 WOS Scopus РИНЦ OpenAlex
Algebras of binary formulas for $\aleph_0$-categorical weakly circularly minimal theories: monotonic case
Вестник Карагандинского университета. Серия Математика (Bulletin of the Karaganda University-Mathematics). 2024. V.113. N1. P.112-127. DOI: 10.31489/2024M1/112-127 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Sep 17, 2023 |
| Accepted: | Dec 4, 2023 |
| Published print: | Mar 29, 2024 |
| Published online: | Mar 29, 2024 |
Identifiers:
| Web of science: | WOS:001196276300012 |
| Scopus: | 2-s2.0-85191583752 |
| Elibrary: | 67356066 |
| OpenAlex: | W4393344952 |