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<p>We introduce a new weak variation of diamond that is meant to guess only the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by proving it is compatible with Martin’s axiom. We then prove that this principle is nontrivial by showing it may consistently fail.</p>

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Diamond on Kurepa trees

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月28日

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  • Ziemowit Kostana,
  • Assaf Rinot,
  • Saharon Shelah

摘要

We introduce a new weak variation of diamond that is meant to guess only the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by proving it is compatible with Martin’s axiom. We then prove that this principle is nontrivial by showing it may consistently fail.