Spherically complete models of Hensel minimal valued fields

TL;DR

This paper demonstrates that certain Hensel minimal valued fields can be extended to spherically complete models, providing a deeper understanding of their structure and elementary extensions.

Contribution

It establishes the existence of spherically complete immediate elementary extensions for Hensel minimal expansions of finitely ramified Henselian valued fields.

Findings

Hensel minimal expansions admit spherically complete immediate extensions

The work applies to finitely ramified Henselian valued fields

Uses $0$-hmix-minimality in equi-characteristic 0

Abstract

We prove that Hensel minimal expansions of finitely ramified Henselian valued fields admit spherically complete immediate elementary extensions. More precisely, the version of Hensel minimality we use is $0$-hmix-minimality (which, in equi-characteristic $0$, amounts to $0$-h-minimality).