关于边界数、分裂数和分配数
On the bounding, splitting, and distributivity numbers
摘要：
已知$\mathcal P (ω)$的基数不变量$ \mathfrak h, \mathfrak b, \mathfrak s$满足该$ω_1 \leq \mathfrak h \leq\min\{\mathfrak b, \mathfrak s\}$。我们证明了所有的不等式都是严格的。我们还介绍了一个新的上界为$\mathfrak h$，并表明它可以小于$\mathfrak s$。其关键是利用ccc偏序集的有限支撑矩阵迭代方法，迭代过程遵循\cite{BlassShelah} .
英文摘要：
The cardinal invariants $ \mathfrak h, \mathfrak b, \mathfrak s$ of $\mathcal P (ω)$ are known to satisfy that $ω_1 \leq \mathfrak h \leq\min\{\mathfrak b, \mathfrak s\}$. We prove that all inequalities can be strict. We also introduce a new upper bound for $\mathfrak h$ and show that it can be less than $\mathfrak s$. The key method is to utilize finite support matrix iterations of ccc posets following \cite{BlassShelah}.
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