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<p>We precisely identify the extent of determinacy provable in Zermelo–Fraenkel set theory with the Axiom of Choice from the hypothesis that <i>x</i><sup>#</sup> exists for every <i>x</i> ∈ ℝ, isolating an optimal strengthening of the Martin–Harrington Determinacy Transfer Theorem in a strong sense.</p>

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Determinacy from sharps

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月21日

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  • Juan P. Aguilera

摘要

We precisely identify the extent of determinacy provable in Zermelo–Fraenkel set theory with the Axiom of Choice from the hypothesis that x# exists for every x ∈ ℝ, isolating an optimal strengthening of the Martin–Harrington Determinacy Transfer Theorem in a strong sense.