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arXiv · 2412.10764

Relative differential closure in Hardy fields

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

We study relative differential closure in the context of Hardy fields. Using our earlier work on algebraic differential equations over Hardy fields, this leads to a proof of a conjecture of Boshernitzan (1981): the intersection of all maximal analytic Hardy fields agrees with that of all maximal Hardy fields. We also generalize a key ingredient in the proof, and describe a cautionary example delineating the boundaries of its applicability.

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Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven. 2024-12-14. Relative differential closure in Hardy fields. https://doi.org/10.1007/s00605-025-02077-y

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