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<p>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.</p>

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Constructing ω-free Hardy fields

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月19日

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

摘要

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.