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<p>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 (J. Anal. Math. <b>39</b>, 235–255, 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.</p>

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Relative differential closure in Hardy fields

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月24日

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

摘要

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 (J. Anal. Math. 39, 235–255, 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.