NIP henselian valued fields

2016/06/27 by Franziska Jahnke, Pierre Simon, Jahnke, Franziska +1
Mathematics · #03C45 #12L12 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1606.08472

openalex publication_date 2016/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that any theory of tame henselian valued fields is NIP if and only if the theory of its residue field and the theory of its value group are NIP. Moreover, we show that if (K,v) is a henselian valued field of residue characteristic char(Kv)=p for which K^×/(K^×)^p is finite in case p>0, then (K,v) is NIP iff Kv is NIP and v is roughly tame.

Citations

• Valued difference fields and NTP2

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