Dp-finite fields VI: the dp-finite Shelah conjecture
Logic
2020-05-29 v1
Abstract
We prove the dp-finite case of the Shelah conjecture on NIP fields. If K is a dp-finite field, then K admits a non-trivial definable henselian valuation ring, unless K is finite, real closed, or algebraically closed. As a consequence, the conjectural classification of dp-finite fields holds. Additionally, dp-finite valued fields are henselian. Lastly, if K is an unstable dp-finite expansion of a field, then K admits a unique definable V-topology.
Keywords
Cite
@article{arxiv.2005.13989,
title = {Dp-finite fields VI: the dp-finite Shelah conjecture},
author = {Will Johnson},
journal= {arXiv preprint arXiv:2005.13989},
year = {2020}
}
Comments
26 pages