English

Distality in valued fields and related structures

Logic 2022-02-22 v3

Abstract

We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian valued fields, and demonstrate that certain expansions of fields, e.g., the differential field of logarithmic-exponential transseries, are distal. As a new tool for analyzing valued fields we employ a relative quantifier elimination for pure short exact sequences of abelian groups.

Keywords

Cite

@article{arxiv.2008.09889,
  title  = {Distality in valued fields and related structures},
  author = {Matthias Aschenbrenner and Artem Chernikov and Allen Gehret and Martin Ziegler},
  journal= {arXiv preprint arXiv:2008.09889},
  year   = {2022}
}

Comments

70 pp; final version, to appear in Trans. Amer. Math. Soc

R2 v1 2026-06-23T18:02:23.044Z