On logical characterization of henselianity

2007/05/03 by Yimu Yin, Yin, Yimu
Mathematics · #03C10 #12J10 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03C10 #msc:12J10

paper · pdf · doi:10.48550/arxiv.0705.0395

Minor corrections

arxiv created 2007/05/07 · arxiv updated 2009/12/01

Abstract

We give some sufficient conditions under which any valued field that admits quantifier elimination in the Macintyre language is henselian. Then, without extra assumptions, we prove that if a valued field of characteristic (0,0) has a \Z-group as its value group and admits quantifier elimination in the main sort of the Denef-Pas style language L_RRP then it is henselian. In fact the proof of this suggests that a quite large class of Denef-Pas style languages is natural with respect to henselianity.

Related

• Burden of henselian valued fields in the Denef-Pas language
• Eliminating Field Quantifiers in Strongly Dependent Henselian Fields
• Henselianity in the language of rings
• A criterion for p-henselianity in characteristic p
• Uniformly defining p-henselian valuations