论文标题
强迫课程颠覆的迭代定理
Iteration theorems for subversions of forcing classes
论文作者
论文摘要
我们证明了詹森（Jensen）介绍的与子培训和子整数强迫相关的类别的类别的各种迭代定理。在第一部分中，我们使用修订后的可数支持迭代，并表明subproper等级，$ {}^ωΩ$ - $ - 绑定强迫概念，2）subproper类，$ t $ preserving迫使求和概念（$ t $ t $ n $ t $是固定的souslin树）和$ the $ there $ there $ there $ there $ there $ there $ there $ trvice（ $ω_1$ -TREE）具有可计数支持。在第二部分中，我们采用了宫本的良好迭代理论，而不是修订可数的支持。我们表明，这种方法使我们能够在子复杂性和子播放性的定义中删除技术条件，但仍会导致强迫以这种方式保持损失的类，并保留$ω_1$，并且在征收子计算的情况下，请不要添加真实。此外，我们表明，迭代定理的类似物在第一部分中也证明了RCS迭代的效果。
We prove various iteration theorems for forcing classes related to subproper and subcomplete forcing, introduced by Jensen. In the first part, we use revised countable support iterations, and show that 1) the class of subproper, ${}^ωω$-bounding forcing notions, 2) the class of subproper, $T$-preserving forcing notions (where $T$ is a fixed Souslin tree) and 3) the class of subproper, $[T]$-preserving forcing notions (where $T$ is an $ω_1$-tree) are iterable with revised countable support. In the second part, we adopt Miyamoto's theory of nice iterations, rather than revised countable support. We show that this approach allows us to drop a technical condition in the definitions of subcompleteness and subproperness, still resulting in forcing classes that are iterable in this way, preserve $ω_1$, and, in the case of subcompleteness, don't add reals. Further, we show that the analogs of the iteration theorems proved in the first part for RCS iterations hold for nice iterations as well.
