论文标题
科恩保护与独立
Cohen Preservation and Independence
论文作者
论文摘要
我们提供了一般保护定理，用于在可数的支持迭代中保存选择性独立家庭。该定理为文献中的许多结果提供了一个一般框架，其中独立数字$ \ mathfrak {i} $严格低于$ \ mathfrak {c} $，包括麻袋强迫的迭代，米勒分区强迫，$ h $ h $ - $ h $ - $ h $ - 完美树的编码。此外，应用定理，我们表明$ \ mathfrak {i} = \ aleph_1 $在Miller Lite模型中。保存定理的一个重要方面是“ Cohen Preservation”的概念，我们会详细讨论。
We provide a general preservation theorem for preserving selective independent families along countable support iterations. The theorem gives a general framework for a number of results in the literature concerning models in which the independence number $\mathfrak{i}$ is strictly below $\mathfrak{c}$, including iterations of Sacks forcing, Miller partition forcing, $h$-perfect tree forcings, coding with perfect trees. Moreover, applying the theorem, we show that $\mathfrak{i} = \aleph_1$ in the Miller Lite model. An important aspect of the preservation theorem is the notion of "Cohen preservation", which we discuss in detail.
