论文标题
超级滤器和几乎不相关的数字
The ultrafilter and almost disjointness numbers
论文作者
论文摘要
我们证明，每个疯狂的家庭都可以通过保留$ p $ points的适当强迫摧毁。通过此结果，我们证明$ω__{1} = \ mathfrak {u} <\ m athfrak {a，} $解决了近20年的Shelah问题和Brendle问题。我们还将提供一个简单的证据，证明了Blass和Shelah的结果，即不等式$ \ Mathfrak {u <s} $是一致的。
We prove that every MAD family can be destroyed by a proper forcing that preserves $P$-points. With this result, we prove that it is consistent that $ω_{1}=\mathfrak{u}<\mathfrak{a,}$ solving a nearly 20 year old problem of Shelah and a problem of Brendle. We will also present a simple proof of a result of Blass and Shelah that the inequality $\mathfrak{u<s}$ is consistent.
