定常集上的阶梯间隙
Ladder gaps over stationary sets
摘要：
对于平稳集S的子集ω_1和S上的梯形系统C，引入并研究了一类新的间隙C-Hausdorff.我们描述了ZFC的一个强迫模型，其中对于某个平稳集S，对于S上的每个阶梯C，每个间隙包含一个子间隙，该子间隙是C-Hausdorff。但对于Ω_1集减S上的每个阶梯E，存在一个没有子能隙的能隙，即E-Hausdorff能隙。提出了一种新的链条件，称为极化链条件。证明了极化c.c.c. c偏序集的有限支集的迭代仍然是极化c.c.c. c偏序集。
英文摘要：
For a stationary set S subseteq omega_1 and a ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is C-Hausdorff. But for every ladder E over omega_1 setminus S there exists a gap with no subgap that is E-Hausdorff. A new type of chain condition, called polarized chain condition, is introduced. We prove that the iteration with finite support of polarized c.c.c posets is again a polarized c.c.c poset.
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