Suslin树、边界数和划分关系
Suslin trees, the bounding number, and partition relations
摘要：
研究了基数$λ$和序数$α$的不同值的非平衡普通配分关系的形式$λ\rightarrow {(λ, α)}^{2}$.例如，我们表明，对于每一个无限基数$κ,$的$κ^{+}-$ Suslin树的存在意味着$κ^{+} \not\rightarrow {\left( κ^{+}, {\log}_κ(κ^{+}) + 2 \right)}^{2}$。正的划分关系$\mathfrak{b} \rightarrow {(\mathfrak{b}, α)}^{2}$的所有$α< ω_{1}$的边界数$\mathfrak{b}$的一致性也建立了从大基数。
英文摘要：
We investigate the unbalanced ordinary partition relations of the form $λ\rightarrow {(λ, α)}^{2}$ for various values of the cardinal $λ$ and the ordinal $α$. For example, we show that for every infinite cardinal $κ,$ the existence of a $κ^{+}-$Suslin tree implies $κ^{+} \not\rightarrow {\left( κ^{+}, {\log}_κ(κ^{+}) + 2 \right)}^{2}$. The consistency of the positive partition relation $\mathfrak{b} \rightarrow {(\mathfrak{b}, α)}^{2}$ for all $α< ω_{1}$ for the bounding number $\mathfrak{b}$ is also established from large cardinals.
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