Joint work with Ziemek Kostana and Saharon Shelah.
Abstract. 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.
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Update August 2024: Extended the introduction.
Submitted to Monatshefte für Mathematik, August 2024.
A referee was assigned, July 2025.
A report was received and a revision was subsequently made, January 2026.
The paper was accepted for publication, March 2026.