发表机构
University of Novi Sad; Freie Universität Berlin（诺维萨德大学; 柏林自由大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文借助他人关于特定有限完全边标记图弗赖斯极限不具有限大拉姆齐度的结果，运用范畴机制，将其结果从边标记图背景转移到群背景，从而证明霍尔通用群不具有有限大拉姆齐度。
AI 中文摘要
在本文中，我们证明了霍尔通用群不具有有限大拉姆齐度。我们的策略是借助胡比奇卡、科内čný、托多罗维奇和祖克（在EUROCOMB 2025上宣布）的最新结果，即所有有限完全边标记图（其标记集为可数无限）的弗赖斯极限不具有有限大拉姆齐度。然后，我们使用范畴机制将他们的结果从边标记图的背景转移到群的背景。
英文摘要
In this paper we show that the Hall's universal group does not have finite big Ramsey degrees. Our strategy consists of piggybacking on the recent result of Hubička, Konečný, Todorčević and Zucker (announced at EUROCOMB 2025) that the random edge-labelled graph (the Fraïssé limit of the class of all finite complete edge-labelled graphs where the set of labels is countably infinite) does not have finite big Ramsey degrees. We then use the machinery of category theory to transport this result from the context of edge-labelled graphs to the context of groups. The main step in the process is the construction of a functor from the category of edge-labelled graphs and embeddings to the category of groups and group embeddings which takes finite graphs to finite groups. This makes is possible for us to build a subgroup of the Hall's universal group which encodes the random edge-labelled graph. Our main result shows that several families finite groups, including non-cyclic abelian groups, do not have finite big Ramsey degrees in the Hall's universal group. Actually, we show that all potential candidates for groups with finite big Ramsey degrees have to be solvable.
