Constructing ω-free Hardy fields

Matthias Aschenbrenner; Lou van den Dries; Joris van der Hoeven

doi:10.1007/s11854-026-0447-y

Constructing ω-free Hardy fields

Matthias Aschenbrenner
, Lou van den Dries
, Joris van der Hoeven

University of Vienna
University of Illinois at Urbana-Champaign

Research output: Contribution to journal › Article › peer-review

Abstract

We show that every Hardy field extends to an ω-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.

Original language	English
Journal	Journal d'Analyse Mathematique
DOIs	https://doi.org/10.1007/s11854-026-0447-y
Publication status	Accepted/In press - 1 Jan 2026

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Constructing ω-free Hardy fields

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