Henselianity in the language of rings

Sylvy Anscombe; Franziska Jahnke

Henselianity in the language of rings

Logic 2015-12-16 v1

Authors: Sylvy Anscombe , Franziska Jahnke

Abstract

We consider four properties of a field $K$ related to the existence of (definable) henselian valuations on $K$ and on elementarily equivalent fields, and study the implications between them. Surprisingly, the full pictures look very different in equicharacteristic and mixed characteristic.

Keywords

henselian valuation field theory model theory equicharacteristic mixed characteristic definable valuation elementary equivalence

Cite

@article{arxiv.1512.04588,
  title  = {Henselianity in the language of rings},
  author = {Sylvy Anscombe and Franziska Jahnke},
  journal= {arXiv preprint arXiv:1512.04588},
  year   = {2015}
}

Comments

18 pages

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