论文标题
鳍与疯狂的家庭
Fin-intersecting MAD families
论文作者
论文摘要
我们介绍了一个新的几乎不相交的家庭，我们称之为鳍上几乎不相交的家庭。它们与几乎不相关的家庭有关，他们的越野越多的Isbell-Mrówka空间是假发的。我们表明，在$ \ Mathfrak p = \ mathfrak c $ fin的疯狂家庭中，它们普遍存在，如果$ \ mathfrak {a <s} $，它们也存在，但是在ZFC中也有非鳍式的疯狂家庭。我们还表明，在CH下，存在鳍与疯狂的家庭相交，它们在添加了任意数量的Cohen Real和随机真实的情况下仍然存在。这些结果提供了更多的模型，其中存在伪造的疯狂家庭。
We introduce a new class of almost disjoint families which we call fin-intersecting almost disjoint families. They are related to almost disjoint families whose Vietoris Hyperspace of their Isbell-Mrówka spaces are pseudocompact. We show that under $\mathfrak p=\mathfrak c$ fin-intersecting MAD families exist generically and they also exist if $\mathfrak{a<s}$, but that there are also non fin-intersecting MAD families in ZFC. We also show that under CH, there exists fin intersecting MAD families which remain like that after adding an arbitrary quantity of Cohen reals and Random reals. These results give more models in which pseudocompact MAD families exist.
