论文标题
边缘色和树木的注释
A Note on Edge Colorings and Trees
论文作者
论文摘要
我们指出了某些边缘着色的同质集的存在与某些树木中分支的存在之间的一些联系。结果，我们得到红衣主教$κ$的任何本地添加色（论文中引入的概念）都有一组均匀的$κ$，但前提是$μ$ $μ^+<κ$。另一个结果是，如果$κ$是常规的，具有$λ<κ$，则存在$κ^*<κ$，因此，只有$κ$是常规的，每个$κ^*<κ$，因此每一个高度$μ$ $λ$ nodes的$κ^*$ nodes都少于$κ^*$ brounch。
We point out some connections between existence of homogenous sets for certain edge colorings and existence of branches in certain trees. As a consequence, we get that any locally additive coloring (a notion introduced in the paper) of a cardinal $κ$ has a homogeneous set of size $κ$ provided that the number of colors, $μ$ satisfies $μ^+<κ$. Another result is that an uncountable cardinal $κ$ is weakly compact if and only if $κ$ is regular, has the tree property and for each $λ,μ<κ$ there exists $κ^*<κ$ such that every tree of height $μ$ with $λ$ nodes has less than $κ^*$ branches.
