# Maximal immediate extensions of valued differential fields

## TL;DR

This paper proves that every valued differential field can be extended to a spherically complete immediate extension and discusses the conditions for its uniqueness up to isomorphism.

## Contribution

It establishes the existence of maximal immediate spherically complete extensions for valued differential fields and analyzes their uniqueness.

## Key findings

- Existence of immediate spherically complete extensions for valued differential fields.
- Discussion on the uniqueness of these extensions up to isomorphism.

## Abstract

We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.