Short Hardy fields
Logic
2025-08-11 v1 Commutative Algebra
Classical Analysis and ODEs
Number Theory
Abstract
Differentially algebraic Hardy field extensions of short Hardy fields are short. This is proved in the more general setting of -fields. As an application we extend a theorem of Rosenlicht (1981) by showing that each short asymptotic couple of Hardy type with small derivation is isomorphic to the asymptotic couple of an analytic Hardy field.
Keywords
Cite
@article{arxiv.2508.06161,
title = {Short Hardy fields},
author = {Matthias Aschenbrenner and Lou van den Dries},
journal= {arXiv preprint arXiv:2508.06161},
year = {2025}
}
Comments
13 pp