An Ax-Kochen-Ershov Theorem for Monotone Differential-Henselian Fields

TL;DR

This paper extends Ax-Kochen-Ershov theorems to monotone differential-henselian fields by removing the previously required condition of having many constants, broadening the theorem's applicability.

Contribution

It provides a new proof that eliminates the 'many constants' condition in Ax-Kochen-Ershov results for differential-henselian monotone valued differential fields.

Findings

Removed the 'many constants' condition from existing theorems

Extended the applicability of Ax-Kochen-Ershov results

Provided a new proof technique for differential-henselian fields

Abstract

Scanlon [5] proves Ax-Kochen-Ershov type results for differential-henselian monotone valued differential fields with many constants. We show how to get rid of the condition "with many constants".