On algebras of binary isolating formulas for weakly circularly minimal theoriesof convexity rank 2
DOI:
https://doi.org/10.70474/kmj24-4-01Keywords:
algebra of binary formulas, ℵ0-categorical theory, weak circular minimality, circularly ordered structure, convexity rankAbstract
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 non-primitive 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.
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