English

Distality in Ordered Abelian Groups

Logic 2026-02-27 v1

Abstract

We provide a characterization of distal ordered abelian groups: An ordered abelian group is distal if and only if, for each prime number pp, the sizes of ribs with respect to the "valuation" sp\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.

Keywords

Cite

@article{arxiv.2602.23256,
  title  = {Distality in Ordered Abelian Groups},
  author = {Koki Okura},
  journal= {arXiv preprint arXiv:2602.23256},
  year   = {2026}
}

Comments

21 pages

R2 v1 2026-07-01T10:54:16.110Z