Henselian valued fields and inp-minimality

TL;DR

This paper proves that ultraproducts of p-adic fields and certain Henselian valued fields of equicharacteristic zero are inp-minimal, extending model-theoretic understanding of these valued fields' complexity.

Contribution

It establishes inp-minimality for ultraproducts of p-adic fields and generalizes this to Henselian valued fields of equicharacteristic zero using an Ax-Kochen type result.

Findings

Ultraproducts of p-adic fields are inp-minimal.

Inp-minimality is preserved in Henselian valued fields of equicharacteristic zero.

Provides a model-theoretic characterization of these valued fields.

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.