c-Regular cyclically ordered groups
G\'erard Leloup (LMM), Francois Lucas (LAREMA)

TL;DR
This paper characterizes regular and c-regular cyclically ordered abelian groups, showing their elementary equivalences to well-known structures like complex roots of unity, finite cyclic groups, and integers.
Contribution
It introduces the concepts of regular and c-regular cyclically ordered abelian groups and establishes their elementary equivalences to classical algebraic structures.
Findings
Dense c-regular groups are elementarily equivalent to complex roots of unity.
Discrete c-regular groups are elementarily equivalent to ultraproducts of finite cyclic groups.
Regular non-c-regular groups are elementarily equivalent to the integers.
Abstract
We define and we characterize regular and c-regular cyclically ordered abelian groups. We prove that every dense c-regular cyclically ordered abelian group is elementarily equivalent to some cyclically ordered group of unimodular complex numbers, that every discrete c-regular cyclically ordered abelian group is elementarily equivalent to some ultraproduct of finite cyclic groups, and that the discrete regular non-c-regular cyclically ordered abelian groups are elementarily equivalent to the linearly cyclically ordered group of integers.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topology and Set Theory · Advanced Algebra and Logic
