论文标题
Ramsey关于分区的理论II：负面关系和泵送定理
Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems
论文作者
论文摘要
在这一系列论文中，我们将拉姆齐色彩理论推向了分区。在这一部分中，我们专注于反兰西的关系，或者，众所周知，它们的着色是强烈的，尤其是从[CKS21]中解决了两个问题。 结果表明，对于每个无限的红衣主教$λ$，可以将分区上的$λ^+$上的颜色强给$λ$的颜色，可以用$λ^{+} $颜色在同一分区上延伸到一个颜色。同样，对于一个较强的颜色，可以改善$ pr_1（\ ldots）$的浓烈着色时，可以改善有足够的条件。 由于经典理论对应于仅一个单元的分区的特殊情况，因此两个结果分别概括了由于Eisworth和Shelah引起的泵送定理。
In this series of papers we advance Ramsey theory of colorings over partitions. In this part, we concentrate on anti-Ramsey relations, or, as they are better known, strong colorings, and in particular solve two problems from [CKS21]. It is shown that for every infinite cardinal $λ$, a strong coloring on $λ^+$ by $λ$ colors over a partition can be stretched to one with $λ^{+}$ colors over the same partition. Also, a sufficient condition is given for when a strong coloring witnessing $Pr_1(\ldots)$ over a partition may be improved to witness $Pr_0(\ldots)$. Since the classical theory corresponds to the special case of a partition with just one cell, the two results generalize pump-up theorems due to Eisworth and Shelah, respectively.
