This article is cited in 3 papers

Algebras of binary formulas for weakly circularly minimal theories with trivial definable closure

B. Sh. Kulpeshov<sup>ab

a</sup> Kazakh-British Technical University
^b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty

Abstract: We describe the algebras of binary formulas for countably categorical weakly circularly minimal theories with 1-transitive nonprimitive automorphism group and trivial definable closure having convexity rank 1. We find some criterion for commutativity of the algebras.

Keywords: algebra of binary formulas, countably categorical theory, weak circular minimality, circularly ordered structure.

UDC: 510.67

MSC: 35R30

Received: 23.11.2022
Revised: 15.05.2023
Accepted: 28.01.2024

DOI: 10.33048/smzh.2024.65.207

 English version: Siberian Mathematical Journal, 2024, 65:2, 316–327