平稳反射与SCH的失败
Stationary Reflection and the failure of SCH
AI总结：
本文证明从大基数出发，奇异基数假设在奇异强极限基数$ν$处失败且平稳子集同时反射的情况是相容的，并降低了$\mathrm{cf}(ν)=ω$时的相容性强度上界。
摘要：
在本文中，我们证明从大基数出发，以下情况是相容的：存在奇异强极限基数$ν$，使得奇异基数假设在$ν$处失败，并且$ν^+$的少于$\mathrm{cf}(ν)$个平稳子集的每个集合同时反射。对于$\mathrm{cf}(ν) > ω$，这种情况以前未被知晓是相容的。使用不同方法，我们将$\mathrm{cf}(ν) = ω$时这种情况的相容性强度上界降低到一个部分超紧基数以下。先前由Sharon给出的无穷多超紧基数上界被取代。
英文摘要：
In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal $ν$ such that the singular cardinal hypothesis fails at $ν$ and every collection of fewer than $\mathrm{cf}(ν)$ stationary subsets of $ν^+$ reflects simultaneously. For $\mathrm{cf}(ν) > ω$, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for $\mathrm{cf}(ν) = ω$ to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
