We show that the universal homogeneous partial order has finite big Ramsey degrees and discuss several corollaries. Our proof uses parameter spaces and the Carlson-Simpson theorem rather than (a strengthening of) the Halpern-L\"auchli theorem and the Milliken tree theorem, which are the primary tools used to give bounds on big Ramsey degrees elsewhere (originating from work of Laver and Milliken). This new technique has many additional applications. To demonstrate this, we show that the homogeneous universal triangle-free graph has finite big Ramsey degrees, thus giving a short proof of a recent result of Dobrinen.

中文翻译：

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使用参数空间的大拉姆齐度

我们证明了普遍齐次偏序具有有限的大 Ramsey 度并讨论了几个推论。我们的证明使用参数空间和 Carlson-Simpson 定理，而不是（强化）Halpern-L\"auchli 定理和 Milliken 树定理，它们是用于在其他地方（源自工作）给出大拉姆齐度数界限的主要工具Laver 和 Milliken）。这项新技术有许多额外的应用。为了证明这一点，我们证明了齐次通用无三角形图具有有限的大 Ramsey 度，从而对 Dobrinen 的最近结果进行了简短的证明。