Recent Progress on Definability of Henselian Valuations

2016/08/08 by Fehm, Arno, Jahnke, Franziska · 2 citations
#12E30 #12L12 #FOS: Mathematics #Logic (math.LO) #Primary: 12J10 #secondary: 03C60

paper · doi:10.48550/arxiv.1608.02342

Abstract

Although the study of the definability of henselian valuations has a long history starting with J. Robinson, most of the results in this area were proven during the last few years. We survey these results which address the definability of concrete henselian valuations, the existence of definable henselian valuations on a given field, and questions of uniformity and quantifier complexity.

Cited by

• Construction of a valued field whose valuation ring is definable but neither ∃∀∃ nor ∀∃∀-definable in the language of rings
• Definable ranks

Related

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• A definable henselian valuation with high quantifier complexity
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• Definable henselian valuations on dp-minimal real fields