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arXiv · 2508.06161

Short Hardy fields

Matthias Aschenbrenner·Lou van den Dries
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Abstract

Differentially algebraic Hardy field extensions of short Hardy fields are short. This is proved in the more general setting of $H$-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.

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BibTeXRIS

Matthias Aschenbrenner, Lou van den Dries. 2025-08-08. Short Hardy fields. https://arxiv.org/abs/2508.06161

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