The Ax-Kochen-Ershov principles via the higher valued hyperfield

TL;DR

This paper explores the model theory of finitely ramified henselian valued fields using higher valued hyperfields, establishing Ax-Kochen-Ershov principles and transfer results for decidability.

Contribution

It introduces Ax-Kochen-Ershov theorems for these fields relative to higher valued hyperfields, advancing the understanding of their logical properties.

Findings

Established Ax-Kochen-Ershov theorems for finitely ramified henselian valued fields

Proved transfer of decidability for full and existential theories

Connected model theory of valued fields with higher valued hyperfields

Abstract

In this paper, we concern the model theory of finitely ramified henselian valued fields via higher valued hyperfields. Most of all, we provide a number of Ax-Kochen-Ershov Theorems for finitely ramified henselian valued fields relative to higher valued hyperfields. As corollaries, we deduce a transfer of decidability for full theories and existential theories of a finitely ramified henselian valued fields relative to higher valued hyperfields.