Constructing $\omega$-free Hardy fields
Commutative Algebra
2026-03-11 v3 Classical Analysis and ODEs
Dynamical Systems
Logic
Abstract
We show that every Hardy field extends to an -free Hardy field. This result relates to classical oscillation criteria for second-order homogeneous linear differential equations. It is essential in [10], and here we apply it to answer questions of Boshernitzan, and to generalize a theorem of his.
Keywords
Cite
@article{arxiv.2404.03695,
title = {Constructing $\omega$-free Hardy fields},
author = {Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven},
journal= {arXiv preprint arXiv:2404.03695},
year = {2026}
}
Comments
51 pp.; revised following remarks by a referee; to appear in J. Analyse Math