论文标题
关于高度连接且连接良好的拉姆西理论的注释
A note on highly connected and well-connected Ramsey theory
论文作者
论文摘要
我们研究了Bergfalk-Hrušák-Shelah和Bergfalk最近引入的一对经典分区关系$ν\ rightarrow（μ）^2_λ$的弱点。考虑到$ν$ - 许多顶点上完整的图形的边缘色，这些弱点声称存在单色子图的存在，表现出具有很高的连接度的高度，而不是由经典关系所占据的完整单色子学。结果，这些弱点的版本可以始终如一地保持在可访问的红衣主教中，在这些红衣主教中，它们的经典类似物必然会失败。我们证明了一些互补的阳性和负面结果，表明大型红衣主教，迫使公理和平方原理对这些分区关系的影响。我们还证明了一致性结果，表明这两个分区关系的较强实例可以在连续体中保持。
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.
