P（ω）/fin中的自由序列
Free sequences in P(ω)/fin
摘要：
本文研究了布尔代数$\mathcal{P}(ω)/\mathrm{fin}$中的极大自由序列。寻幂梦想我们提供了一些信息，这些对象的一般结构，我们特别感兴趣的最小基数的一个自由序列，一个基数特性的连续表示$\mathfrak{f}$。针对Monk的一个问题，证明了$ω_1 = \mathfrak{i} = \mathfrak{f} < \mathfrak{u} = ω_2$的相容性.事实上，这种一致性在S. $\mathfrak{i} < \mathfrak{u}$的希拉。我们的文件提供了一个精简的，主要是自我包含的介绍，这一建设。
英文摘要：
We investigate maximal free sequences in the Boolean algebra $\mathcal{P}(ω)/\mathrm{fin}$, as defined by D. Monk. We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted $\mathfrak{f}$. Answering a question of Monk, we demonstrate the consistency of $ω_1 = \mathfrak{i} = \mathfrak{f} < \mathfrak{u} = ω_2$. In fact, this consistency is demonstrated in the model of S. Shelah for $\mathfrak{i} < \mathfrak{u}$. Our paper provides a streamlined and mostly self contained presentation of this construction.
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