Abstract: This paper is devoted to the study of weakly circularly minimal circularly ordered structures. The simplest example of a circular order is a linear order with endpoints, in which the largest element is identified with the smallest. Another example is the order that arises when going around a circle. A circularly ordered structure is called weakly circularly minimal if any of its definable subsets is a finite union of convex sets and points. A theory is called weakly circularly minimal if all its models are weakly circularly minimal. Algebras of binary isolating formulas are described for ℵ0-categorical 1-transitive nonprimitive weakly circularly minimal theories of convexity rank 2 with a trivial definable closure having a monotonic-to-right function to the definable completion of a structure and non-having a non-trivial equivalence relation partitioning the universe of a structure into finitely many convex classes.

Cite: Kulpeshov B.S. , Sudoplatov S.V.
On algebras of binary isolating formulas for weakly circularly minimal theories of convexity rank 2
Kazakh Mathematical Journal. 2024. V.24. N4. P.6-21. DOI: 10.70474/kmj24-4-01 РИНЦ OpenAlex

Dates:

Submitted:	Dec 17, 2024
Accepted:	Dec 23, 2024
Published print:	Dec 30, 2024
Published online:	Dec 30, 2024

Identifiers:

Elibrary:	80981196
OpenAlex:	W4405922717

Citing: Пока нет цитирований

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