论文标题
产品的Ramsey属性和类别的回调和Grothendieck构造
Ramsey properties of products and pullbacks of categories and the Grothendieck construction
论文作者
论文摘要
在本文中，我们提供了纯粹的分类证据，证明了结构性拉姆西理论的两个重要结果：M. \sokić的结果，Ramsey类的免费产品是Ramsey班级，M。\ Bodirsky，M。Xinsker和T. \ T. \ T. \ Tsankov的结果为Ramsey Classe the Ramsey Preserves the Ramsey Presserves the Ramsey Presserves the Ramsey Preserves the Ramsey Preserty the Ramsey Preserty the Ramsey Preserty。我们这里提供的证据忽略了这些陈述的模型理论背景。相反，他们专注于可以构建类的分类结构，并沿途概括原始陈述。事实证明，尽管原始证明策略的基本基础，对关系结构类别的限制与陈述本身无关。我们在此提供的分类证据删除了对一阶结构签名的所有限制，不仅提供有关Ramsey属性的信息，还提供有关Ramsey学位的信息。
In this paper we provide purely categorical proofs of two important results of structural Ramsey theory: the result of M.\ Sokić that the free product of Ramsey classes is a Ramsey class and the result of M.\ Bodirsky, M.\Pinsker and T.\ Tsankov that adding constants to the language of a Ramsey class preserves the Ramsey property. The proofs that we present here ignore the model-theoretic background of these statements. Instead, they focus on categorical constructions by which the classes can be constructed, generalizing the original statements along the way. It turns out that the restriction to classes of relational structures, although fundamental for the original proof strategies, is not relevant for the statements themselves. The categorical proofs we present here remove all the restrictions on the signature of first-order structures and provide the information not only about the Ramsey property but also about the Ramsey degrees.
