论文标题
带有SDAP+的Fraisse结构，第二部分：简单地描述了大拉姆西结构
Fraisse structures with SDAP+, Part II: Simply characterized big Ramsey structures
论文作者
论文摘要
这是关于Fraisse结构的Ramsey特性的两部分系列的第二部分，该结构满足了SDAP+的属性，该属性增强了分离式合并性能。在第一部分中，我们证明，每个有限的关系语言中的每个弗拉伊斯结构都具有任何满足此属性的有限态度的关系符号。在第二部分中，我们证明，每个有限的关系语言中的每个弗拉伊斯结构最多都有两个具有该属性的关系符号，具有有限的大拉姆西学位，具有简单的特征。因此，任何这样的Fraisse结构都承认了一个很大的拉姆西结构。第二部分利用了第I部分中开发的1型树的编码树和第一部分定理的概念，该概念在本文中充当了归纳论证的鸽子洞穴原理。我们的方法可以直接表征该学位，而无需吸引“信封”的标准方法。这项工作为拉姆西理论提供了一种简化而统一的方法，这些方法在一些看似不同的弗莱斯结构类别上。
This is Part II of a two-part series regarding Ramsey properties of Fraisse structures satisfying a property called SDAP+, which strengthens the Disjoint Amalgamation Property. In Part I, we prove that every Fraisse structure in a finite relational language with relation symbols of any finite arity satisfying this property is indivisible. In Part II, we prove that every Fraisse structure in a finite relational language with relation symbols of arity at most two having this property has finite big Ramsey degrees which have a simple characterization. It follows that any such Fraisse structure admits a big Ramsey structure. Part II utilizes the notion of coding trees of 1-types developed in Part I and a theorem from Part I which functions as a pigeonhole principle for induction arguments in this paper. Our approach yields a direct characterization of the degrees without appeal to the standard method of "envelopes". This work offers a streamlined and unifying approach to Ramsey theory on some seemingly disparate classes of Fraisse structures.
