论文标题
通用逆极限结构中的大拉姆西学位
Big Ramsey degrees in universal inverse limit structures
论文作者
论文摘要
我们建立了一系列拓扑拉姆西树木空间的集合，从而产生了普遍的逆限制结构，将郑的工作扩展到fra \“ fra \”的设置，“有限的有限订购的二进制关系结构与拉姆西属性。这项工作基于Halpern-LäuchliTheorem and subse and subse sumse and subse and subse of subse and subse of subse and subse。 Huber-guschke-kojman在有限有限的图的逆极限上，我们证明，对于每个这样的fra \“ıssé类），其通用的倒数限制结构在有限的baire-leasealable-Measealable-Measealable-Measealable colorings下具有有限的大拉姆西学位。对于满足自由合并以及有限的订购比赛和有限的部分订单的\ fraisse \类，我们表征了确切的大拉姆西学位。
We build a collection of topological Ramsey spaces of trees giving rise to universal inverse limit structures,extending Zheng's work for the profinite graph to the setting of Fra\"ıssé classes of finite ordered binary relational structures with the Ramsey property. This work is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. Based on these topological Ramsey spaces and the work of Huber-Geschke-Kojman on inverse limits of finite ordered graphs, we prove that for each such Fra\"ıssé class, its universal inverse limit structure has finite big Ramsey degrees under finite Baire-measurable colorings. For such \Fraisse\ classes satisfying free amalgamation as well as finite ordered tournaments and finite partial orders with a linear extension, we characterize the exact big Ramsey degrees.
