关于高连通和良连通拉姆齐理论的一个注记
A note on highly connected and well-connected Ramsey theory
摘要：
本文研究了Bergfalk-Hrušák-Shelah和Bergfalk最近分别引入的经典配分关系$ν\rightarrow (μ)^2_λ$的一对弱化.给定完全图在$ν$ -多个顶点上的边染色，这些弱化断言存在表现出高度连通性的单色子图，而不是经典关系所断言的存在完全单色子图.因此，这些弱化的版本可以始终保持在可接近的基数上，而它们的经典类似物必然会失败。我们证明了一些互补的积极和消极的结果表明，这些分区关系的影响，大基数，迫使公理和平方原则。我们还证明了一个一致性的结果表明，这两个分区关系的较强的一个非平凡的例子可以在连续。
英文摘要：
We study a pair of weakenings of the classical partition relation $ν\rightarrow (μ)^2_λ$ recently introduced by Bergfalk-Hrušák-Shelah and Bergfalk, respectively. Given an edge-coloring of the complete graph on $ν$-many vertices, these weakenings assert the existence of monochromatic subgraphs exhibiting high degrees of connectedness rather than the existence of complete monochromatic subgraphs asserted by the classical relations. As a result, versions of these weakenings can consistently hold at accessible cardinals where their classical analogues would necessarily fail. We prove some complementary positive and negative results indicating the effect of large cardinals, forcing axioms, and square principles on these partition relations. We also prove a consistency result indicating that a non-trivial instance of the stronger of these two partition relations can hold at the continuum.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
