Squares and covering matrices
Squares and covering matrices
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平方和覆盖矩阵
DOI：
10.1016/j.apal.2013.10.001
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
C. Lambie
中科院分区：
文献类型：
--
作者：
C. Lambie
Viale在证明SCH遵循PFA的过程中引入了覆盖矩阵。在证明过程和随后与Sharon的工作中，他分离出两个反射原理CP和S，在某些情况下，它们被所有具有特定形状的覆盖矩阵所满足。利用平方序列构造了不满足CP和S的覆盖矩阵。这自然导致了对正则基数κ在□κ和□（κ+）之间的平方原理的研究。我们提供了这些简单原则之间含义的详细图景。
Viale introduced covering matrices in his proof that SCH follows from PFA. In the course of the proof and subsequent work with Sharon, he isolated two reflection principles, CP and S, which, under certain circumstances, are satisfied by all covering matrices of a certain shape. Using square sequences, we construct covering matrices for which CP and S fail. This leads naturally to an investigation of square principles intermediate between□ κ and□(κ+) for a regular cardinal κ. We provide a detailed picture of the implications between these square principles.