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 ${\omega }_1$, we uncover some connections between versions of Chang's Conjectures and instances of rainbow Ramsey partition relations, addressing a question raised in [18].

中文翻译：

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固定和封闭彩虹子集

我们在无数基数上研究结构彩虹Ramsey理论。与通常的Rainbow Ramsey理论相比，该变化集中在寻找不仅具有特定基数而且还满足某些结构性约束（例如在其上端处于静止或闭合）的Rainbow子集。在处理红衣主教大于${\omega }_{\mathrm{1个}}$，我们发现了Chang的猜想版本与Rainbow Ramsey分区关系实例之间的一些联系，从而解决了[18]中提出的问题。