English

Strongly Dependent Ordered Abelian Groups and Henselian Fields

Logic 2024-04-09 v4 Group Theory

Abstract

Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and {p prime:[G:pG]=}<|\{p\text{ prime}:[G:pG]=\infty\}|<\infty. We apply this to show that if KK is a strongly dependent field, then (K,v)(K,v) is strongly dependent for any henselian valuation vv.

Keywords

Cite

@article{arxiv.1706.03376,
  title  = {Strongly Dependent Ordered Abelian Groups and Henselian Fields},
  author = {Yatir Halevi and Assaf Hasson},
  journal= {arXiv preprint arXiv:1706.03376},
  year   = {2024}
}
R2 v1 2026-06-22T20:15:21.224Z