Uniformly defining p-henselian valuations

Author: 

Jahnke, F
Koenigsmann, J

Publication Date: 

1 January 2015

Journal: 

Annals of Pure and Applied Logic

Last Updated: 

2019-08-14T02:25:19.79+01:00

Issue: 

7-8

Volume: 

166

DOI: 

10.1016/j.apal.2015.03.003

page: 

741-754

abstract: 

© 2015 Elsevier B.V. Admitting a non-trivial p-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, p-henselianity is an elementary property in the language of rings. We are interested in the question when a field admits a non-trivial 0-definable p-henselian valuation (in the language of rings). We give a classification of elementary classes of fields in which the canonical p-henselian valuation is uniformly 0-definable. We then apply this to show that there is a definable valuation inducing the (t-)henselian topology on any (t-)henselian field which is neither separably closed nor real closed.

Symplectic id: 

525305

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article