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