2016/07/11 by Franziska Jahnke, Jahnke, Franziska
Economics, Econometrics and Finance · Mathematics · #Advanced Topology and Set Theory #Economic theories and models #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1607.02953
openalex publication_date 2016/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be an NIP field and let v be a henselian valuation on K. We ask whether (K,v) is NIP as a valued field. By a result of Shelah, we know that if v is externally definable, then (K,v) is NIP. Using the definability of the canonical p-henselian valuation, we show that whenever the residue field of v is not separably closed, then v is externally definable. In the case of separably closed residue field, we show that (K,v) is NIP as a pure valued field.