All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)
All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)
复制标题
所有这些 Ramsey 类（带有闭包和禁止同态的 Ramsey 类）
DOI：
10.1016/j.aim.2019.106791
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
J. Nesetril
中科院分区：
文献类型：
--
作者：
J. Hubicka;J. Nesetril
我们证明了具有闭包和给定局部性质的有序结构类的Ramsey性质。这推广了先前的结果：Nešetřil-Rödl定理，偏序和度量空间的Ramsey性质以及作者的无领结图的Ramsey举升。我们使用这个框架解决了几个开放的问题，并给出了Ramsey类的新例子。其中，我们发现了凸序s -度量空间的Ramsey提升，并证明了有限模型（即同时具有函数和关系的结构）的Ramsey定理，从而提供了结构Ramsey定理的最终推广。这两个结果都很自然，也很容易陈述，但它们的证明涉及了这里发展的大部分理论。我们还描述了由有限多个禁止同态定义的结构类的Ramsey提升，并将其扩展到具有闭包的类的特殊情况。这有许多应用。例如，我们发现许多Cherlin-Shelah-Shi类的Ramsey升降机。
We prove the Ramsey property for classes of ordered structures with closures and given local properties. This generalises earlier results: the Nešetřil–Rödl Theorem, the Ramsey property of partial orders and metric spaces as well as the authors' Ramsey lift of bowtie-free graphs. We use this framework to solve several open problems and give new examples of Ramsey classes. Among others, we find Ramsey lifts of convexly orderedS-metric spaces and prove the Ramsey theorem for finite models (i.e. structures with both functions and relations) thus providing the ultimate generalisation of the structural Ramsey theorem. Both of these results are natural, and easy to state, yet their proofs involve most of the theory developed here.We also characterise Ramsey lifts of classes of structures defined by finitely many forbidden homomorphisms and extend this to special cases of classes with closures. This has numerous applications. For example, we find Ramsey lifts of many Cherlin–Shelah–Shi classes.