In this survey paper we collect several known results on destroying tall ideals on countable sets and maximal almost disjoint families with forcing. In most cases we provide streamlined proofs of the presented results. The paper contains results of many authors as well as a preview of results of a forthcoming paper of Brendle, Guzmán, Hrušák, and Raghavan.

中文翻译：

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理想和MAD家庭的坚不可摧

在这份调查论文中，我们收集了一些已知的结果，这些结果破坏了在可数集合上的高理想以及在强迫作用下最大的几乎不相交的家庭。在大多数情况下，我们提供所提供结果的简化证明。本文包含许多作者的结果，以及即将出版的Brendle，Guzmán，Hrušák和Raghavan的论文的结果预览。