论文标题
预发膨胀的分类概念
A Categorical Notion of Precompact Expansion
论文作者
论文摘要
我们通过功能手段概括了Fraïssé类的关系预跨性扩展的概念，其灵感来自Laflamme，NguyenvanThé和Sauer在密集的本地秩序的纸张分区属性以及Milliken的Theorem theorem arxiv：0710.2885中概述的技术概念。我们还概括了扩展属性，并证明了Ramsey学位的分类预发扩展授予上限。此外，我们在严格的条件下表明，我们还可以计算大拉姆西学位。我们还使用我们的方法来计算所有$ n \ geq 2 $的年龄$ $（\ mathbf {s}（n））$中的对象的大和小小的。
We generalize the notion of relational precompact expansions of Fraïssé classes via functorial means, inspired by the technique outlined by Laflamme, Nguyen Van Thé and Sauer in their paper Partition properties of the dense local order and a colored version of Milliken's theorem arXiv:0710.2885. We also generalize the expansion property and prove that categorical precompact expansions grant upper bounds for Ramsey degrees. Moreover, we show under strict conditions, we can also compute big Ramsey degrees. We also apply our methodology to calculate the big and little Ramsey degrees of the objects in Age$(\mathbf{S}(n))$ for all $n\geq 2$.
