Henselian valued fields and inp-minimality

Abstract

We prove that every ultraproduct of $p$-adics is inp-minimal (i.e., of burden $1$). More generally, we prove an Ax-Kochen type result on preservation of inp-minimality for Henselian valued fields of equicharacteristic $0$ in the RV language.

v.2: 15 pages, minor corrections and presentation improvements; accepted to the Journal of Symbolic Logic