Burden in Henselian valued fields

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 leading term structure. These results are generalisations of Chernikov and Simon's work in [11]. & COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

In this article, we demonstrate that the burden of a Henselian valued field can be determined based on the burden of its residue field and value group, following the Ax-Kochen-Ershov principle. To establish this, we establish that the burden of such a field is equivalent to the burden of its leading term structure. These findings extend the work of Chernikov and Simon in [11].