Strongly unfoldable cardinals made indestructible
Strongly unfoldable cardinals made indestructible
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强烈可展开的红衣主教坚不可摧
DOI：
10.2178/jsl/1230396915
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发表时间：
2008
影响因子：
0.6
通讯作者：
Thomas A. Johnstone
中科院分区：
文献类型：
--
作者：
Thomas A. Johnstone
摘要本文给出了满足V = L的大基数的不灭性结果，如弱紧、不可描述和强不可折叠的基数。主要定理表明，任何强不可折叠基数κ都可以通过<κ-闭，κ-真强迫而变得不可破坏。这类偏序集包括所有的<κ-闭偏序集，它们要么是κ−-c. c。或<κ-策略闭以及有限迭代的偏序集。由于强不可折叠基数加强了不可描述基数和弱紧基数，因此主要定理使得这两个大基数概念同样不可摧毁。终于来了我应用主要定理获得了一类强制扩展，该扩展保留了所有强不可折叠基数，其中每个强不可折叠基数κ都不能被<κ-闭的、κ-适当的强制破坏。
Abstract I provide indestructibility results for large cardinals consistent with V = L, such as weakly compact, indescribable and strongly unfoldable cardinals. The Main Theorem shows that any strongly unfoldable cardinal κ can be made indestructible by <κ-closed, κ-proper forcing. This class of posets includes for instance all <κ-closed posets that are either κ−-c.c. or <κ-strategically closed as well as finite iterations of such posets. Since strongly unfoldable cardinals strengthen both indescribable and weakly compact cardinals, the Main Theorem therefore makes these two large cardinal notions similarly indestructible. Finally. I apply the Main Theorem to obtain a class forcing extension preserving all strongly unfoldable cardinals in which every strongly unfoldable cardinal κ is indestructible by <κ-closed, κ-proper forcing.