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arXiv · 2404.03695

Constructing $ω$-free Hardy fields

Matthias Aschenbrenner·Lou van den Dries·Joris van der Hoeven
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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.

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Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven. 2026-03-10. Constructing $ω$-free Hardy fields. https://arxiv.org/abs/2404.03695

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