We introduce the property “F-linked” of subsets of posets for a given free filter F on the natural numbers, and define the properties “μ-F-linked” and “θ-F-Knaster” for posets in a natural way. We show that θ-F-Knaster posets preserve strong types of unbounded families and of maximal almost disjoint families.

Concerning iterations of such posets, we develop a general technique to construct θ-Fr-Knaster posets (where Fr is the Frechet ideal) via matrix iterations of <θ-ultrafilter-linked posets (restricted to some level of the matrix). This is applied to prove consistency results about Cichoń's diagram (without using large cardinals) and to prove the consistency of the fact that, for each Yorioka ideal, the four cardinal invariants associated with it are pairwise different.

At the end, we show that three strongly compact cardinals are enough to force that Cichoń's diagram can be separated into 10 different values.

我们引入财产“ ˚F偏序集为给定的无过滤器的子集-连接” ˚F的自然数，定义属性“ μ - ˚F -连接”和“ θ - ˚F -Knaster”为以自然的方式偏序集。我们证明了θ - F -Knaster球体保留了无界家庭和几乎几乎不相交的家庭的强大类型。

关于此类波状体的迭代，我们开发了一种通用技术，可通过< θ-超滤器链接的波状体（限于矩阵的某些水平）的矩阵迭代来构造θ -Fr-Knaster波状体（其中Fr是Frechet理想）。这用于证明关于Cichoń图的一致性结果（不使用大基数），并证明以下事实的一致性：对于每个Yorioka理想，与之相关的四个基数不变是成对的。

最后，我们展示了三个非常紧凑的基数足以迫使Cichoń的图分成10个不同的值。