Newtonian valued differential fields with arbitrary value group

TL;DR

This paper extends the theory of Newtonian valued differential fields by removing the divisibility assumption on the value group, establishing new results on their structure and extensions.

Contribution

It generalizes existing results on Newtonianity in valued differential fields to arbitrary value groups, removing previous divisibility constraints.

Findings

Removed divisibility assumption on value group

Proved uniqueness of certain differential algebraic extensions

Extended the theory of Newtonian valued differential fields

Abstract

The notion of newtonianity is central to the study of the ordered differential field of logarithmic-exponential transseries done by Aschenbrenner, van den Dries, and van der Hoeven; see Chapter 14 of arxiv:1509.02588. We remove the assumption of divisible value group from two of their results concerning newtonianity, namely the newtonization construction and the equivalence of newtonianity with asymptotic differential-algebraic maximality. We deduce the uniqueness of immediate differentially algebraic extensions that are asymptotically differential-algebraically maximal.