Definable henselian valuations

Author: 

Jahnke, F
Koenigsmann, J

Publication Date: 

29 October 2012

Journal: 

submitted to Journal of Symbolic Logic on 28 Oct 2012

Last Updated: 

2019-08-15T07:11:31.707+01:00

abstract: 

In this note we investigate the question whether a henselian valued field
carries a non-trivial 0-definable henselian valuation (in the language of
rings). It follows from the work of Prestel and Ziegler that there are
henselian valued fields which do not admit a 0-definable non-trivial henselian
valuation. We give conditions on the residue field which ensure the existence
of a parameter-free definiton. In particular, we show that a henselian valued
field admits a non-trivial 0-definable valuation when the residue field is
separably closed or sufficiently non-henselian, or when the absolute Galois
group of the (residue) field is non-universal.

Symplectic id: 

358085

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Submitted to ORA: 

Submitted

Publication Type: 

Journal Article