Stationary reflection principles and two cardinal tree properties
Stationary reflection principles and two cardinal tree properties
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DOI：
10.1017/s1474748013000315
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发表时间：
2013-01
影响因子：
0.9
通讯作者：
Hiroshi Sakai;B. Velickovic
中科院分区：
文献类型：
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作者：
Hiroshi Sakai;B. Velickovic
摘要我们研究了定常和半定常集反射的结果。我们证明了半平稳反射原理蕴含着奇异基数假设、弱平方原理的失败等。我们还考虑了Weiss最近引入的两个基数树性质，并证明了它们是由平稳和半平稳集反射加上马丁公理的一个弱形式而来的。我们还证明了这两个反射原理之间有一些不同，这表明定常集反射类似于超紧性，而半定常集反射类似于强紧性。
Abstract We study the consequences of stationary and semi-stationary set reflection. We show that the semi-stationary reflection principle implies the Singular Cardinal Hypothesis, the failure of the weak square principle, etc. We also consider two cardinal tree properties introduced recently by Weiss, and prove that they follow from stationary and semi-stationary set reflection augmented with a weak form of Martin’s Axiom. We also show that there are some differences between the two reflection principles, which suggests that stationary set reflection is analogous to supercompactness, whereas semi-stationary set reflection is analogous to strong compactness.