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Definable henselian valuations

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 valu...

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Publication date:
2012-10-29
URN:
uuid:19c4390f-009e-4e05-b7b7-fac9ee99f22c
Source identifiers:
358085
Local pid:
pubs:358085

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