论文标题
带有SDAP+的Fraisse结构，第一部分：不可分割性
Fraisse Structures with SDAP+, Part I: Indivisibility
论文作者
论文摘要
这是关于Fraisse结构的Ramsey属性的两部分系列的第一部分，该结构满足了一个名为SDAP+的属性，该属性增强了分离式合并属性。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。新颖性包括在Fraisse结构的初始段的1型方面对树进行的新配方，以及直接证明不可分割性的证明，该证明使用强迫进行无限制搜索有限集的方法。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。第二部分将第一部分的定理用作归纳论点的伪造原则。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 I of a two-part series regarding Ramsey properties of Fraisse structures satisfying a property called SDAP+, which strengthens the Disjoint Amalgamation Property. We prove that every Fraisse structure in a finite relational language with relation symbols of any finite arity satisfying this property is indivisible. Novelties include a new formulation of coding trees in terms of 1-types over initial segments of the Fraisse structure, and a direct proof of indivisibility which uses the method of forcing to conduct unbounded searches for finite sets. 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 a theorem from Part I as a pigeonhole principle for induction arguments. This work offers a streamlined and unifying approach to Ramsey theory on some seemingly disparate classes of Fraisse structures.
