Definable Valuations induced by multiplicative subgroups and NIP Fields
Logic
2018-12-05 v4
Abstract
We study the algebraic implications of the non-independence property (NIP) and variants thereof (dp-minimality) on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a definable henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson's preprint "dp-minimal fields", arXiv: 1507.02745v1, July 2015.
Keywords
Cite
@article{arxiv.1704.02910,
title = {Definable Valuations induced by multiplicative subgroups and NIP Fields},
author = {Katharina Dupont and Assaf Hasson and Salma Kuhlmann},
journal= {arXiv preprint arXiv:1704.02910},
year = {2018}
}
Comments
There was a mistake in Theorem 3.2 (4) of the first arxiv version posted April 10, we corrected it and modified the introduction and section 3 accordingly in the second version, a few other issues are fixed in the third version. The fourth version is a revision according to the referee's comments. To appear in AFML