Newtonian valued differential fields with arbitrary value group

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.