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arXiv · 2602.23256

Distality in Ordered Abelian Groups

Koki Okura
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Abstract

We provide a characterization of distal ordered abelian groups: An ordered abelian group is distal if and only if, for each prime number $p$, the sizes of ribs with respect to the "valuation" $\mathfrak{s}_p$ are uniformly bounded. This generalizes the distality criterion for ordered abelian groups with finite spines given by Aschenbrenner, Chernikov, Gehret, and Ziegler. Furthermore, we prove that every ordered abelian group has a distal expansion, affirmatively answering a conjecture posed by the same authors.

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Koki Okura. 2026-02-26. Distality in Ordered Abelian Groups. https://arxiv.org/abs/2602.23256

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