Newtonian valued differential fields with arbitrary value group
Commutative Algebra
2020-09-28 v5 Logic
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.
Keywords
Cite
@article{arxiv.1805.01423,
title = {Newtonian valued differential fields with arbitrary value group},
author = {Nigel Pynn-Coates},
journal= {arXiv preprint arXiv:1805.01423},
year = {2020}
}
Comments
9 pages; v5: minor clarifications; v3 corresponds to the published version