Article · The Bulletin of Irkutsk State University Series Mathematics · January 1, 2026
Algebras of Binary Formulas for Weakly Circularly Minimal Theories with Trivial Definable Closure: Monotonic-to-right Case
A. B. Altayeva, B. Sh. Kulpeshov, Sergey Vladimirovich Sudoplatov
Abstract
This article concerns the notion of weak circular minimality being a variant of o-minimality for circularly ordered structures. We consider the binary level of these structures forming algebras of binary isolating formulas, which are based on families of labels and compositions of related formulas. These algebras are studied for ℵ0-categorical 1-transitive non-primitive weakly circularly minimal theories of convexity rank greater than 1 with a trivial definable closure having a non-trivial monotonic-to-right function to the definable completion of a structure. On the basis of the study, the authors present a description of these algebras. It is shown that for this case there exist only commutative algebras. A strict 𝑠-deterministicity of such algebras for some natural number 𝑠 is also established.
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