论文标题
关于无法数量的辅助性的单数弱方形的紧凑性
On compactness of weak square at singulars of uncountable cofinality
论文作者
论文摘要
卡明斯（Cummings），工头和马格多尔（Magidor）证明了詹森（Jensen）的正方形原理在$ \aleph_Ω$上是非压缩的，这意味着$ \ square _ {\ aleph_n} $保持$ n <ω$，而$ n <ω$，而$ \ square _ {\alleph_Ω} $失败。我们调查了这种现象是否将其概括为无数级别性的单数的自然问题。令人惊讶的是，我们表明，在一些温和的假设下，弱的正方形原理$ \square_κ^*$实际上是紧凑的，在无法数的辅助性的单数中，这些假设的更强大版本不足以使弱方形的紧凑性在$ \alleph_Ω$处的紧凑性。
Cummings, Foreman, and Magidor proved that Jensen's square principle is non-compact at $\aleph_ω$, meaning that it is consistent that $\square_{\aleph_n}$ holds for all $n<ω$ while $\square_{\aleph_ω}$ fails. We investigate the natural question of whether this phenomenon generalizes to singulars of uncountable cofinality. Surprisingly, we show that under some mild hypotheses, the weak square principle $\square_κ^*$ is in fact compact at singulars of uncountable cofinality, and that an even stronger version of these hypotheses is not enough for compactness of weak square at $\aleph_ω$.
