Burden in Henselian Valued Fields

TL;DR

This paper investigates how the complexity measure called burden in Henselian valued fields can be derived from the burden of their residue fields and value groups, extending previous work by Chernikov and Simon.

Contribution

It establishes that the burden of a Henselian valued field equals the burden of its RV-sort, generalizing prior results and linking field complexity to simpler structures.

Findings

Burden of Henselian valued fields equals the burden of their RV-sort.

Burden can be computed from residue field and value group.

Extends the Ax-Kochen-Ershov principle to burden analysis.

Abstract

In the spirit of the Ax-Kochen-Ershov principle, we show that in certain cases the burden of a Henselian valued field can be computed in terms of the burden of its residue field and that of its value group. To do so, we first see that the burden of such a field is equal to the burden of its RV-sort. These results are generalisations of a work of Chernikov and Simon.