论文标题
使用参数空间的大拉姆西学位
Big Ramsey degrees using parameter spaces
论文作者
论文摘要
我们表明，普遍的同质部分秩序具有有限的大拉姆西学位，并讨论了几个推论。我们的证明依赖于参数空间和Carlson-Simpson定理，而不是（加强）Halpern-Läuchli定理和Milliken Tree Trees定理，这些定理通常用于界定现有文献中的大拉姆西学位（起源于Laver和Milliken的工作）。 这项新技术还有许多其他应用程序。我们表明，均匀的通用三角形图具有有限的大拉姆西学位，提供了Dobrinen最近结果的简短证明。此外，我们概括了NguyenvanThé和Sauer的不可分割性（顶点分区）的结果，我们在有限的距离有限的距离的大拉姆西度量空间上给出了上限。这导致了对Urysohn Sphere的振荡稳定性的新组合论证。
We show that the universal homogeneous partial order has finite big Ramsey degrees and discuss several corollaries. Our proof relies on parameter spaces and the Carlson-Simpson theorem rather than on (a strengthening of) the Halpern-Läuchli theorem and the Milliken tree theorem, which are typically used to bound big Ramsey degrees in the existing literature (originating from the work of Laver and Milliken). This new technique has many additional applications. We show that the homogeneous universal triangle-free graph has finite big Ramsey degrees, providing a short proof of a recent result by Dobrinen. Moreover, generalizing an indivisibility (vertex partition) result of Nguyen van Thé and Sauer, we give an upper bound on big Ramsey degrees of metric spaces with finitely many distances. This leads to a new combinatorial argument for the oscillation stability of the Urysohn Sphere.
