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  1. Usuba’s Principle Can Fail at Singular Cardinals.Mohammad Golshani & Saharon Shelah - 2024 - Journal of Symbolic Logic 89 (1):195-203.
    We answer a question of Usuba by showing that the combinatorial principle $\mathrm {UB}_\lambda $ can fail at a singular cardinal. Furthermore, $\lambda $ can be taken to be $\aleph _\omega.$.
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  • Stationary and closed rainbow subsets.Shimon Garti & Jing Zhang - 2021 - Annals of Pure and Applied Logic 172 (2):102887.
    We study the structural rainbow Ramsey theory at uncountable cardinals. Compared to the usual rainbow Ramsey theory, the variation focuses on finding a rainbow subset that not only is of a certain cardinality but also satisfies certain structural constraints, such as being stationary or closed in its supremum. In the process of dealing with cardinals greater than ω1, we uncover some connections between versions of Chang's Conjectures and instances of rainbow Ramsey partition relations, addressing a question raised in [18].
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