Square in core models
Square in core models
复制标题
核心模型中的正方形
DOI：
10.2307/2687750
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Zeman
中科院分区：
文献类型：
--
作者：
E. Schimmerling;M. Zeman
我们证明了在所有Mitchell-Steel核心模型中，□k对所有k都成立。（见定理2）由此得到了当k是奇异可数闭、弱紧或可测时□k失效的新的一致性强度下界。（推论5、8、9）Jensen引入了一个很大的基本性质，我们称之为次紧性；在大的基数层次结构中，它介于超强度和超紧凑之间。我们证明了在所有Jensen核心模型中，□k在k不是次紧的情况下成立。（见定理15；唯一的if方向本质上是由Jensen决定的。）
We prove that in all Mitchell-Steel core models, □ k holds for all k . (See Theorem 2.) From this we obtain new consistency strength lower bounds for the failure of □ k if k is either singular and countably closed, weakly compact, or measurable. (Corollaries 5, 8, and 9.) Jensen introduced a large cardinal property that we call subcompactness ; it lies between superstrength and supercompactness in the large cardinal hierarchy. We prove that in all Jensen core models, □ k holds iff k is not subcompact. (See Theorem 15; the only if direction is essentially due to Jensen.)