论文标题
炸毁一个奇异的基础级别的基础，倒塌
Blowing up the power of a singular cardinal of uncountable cofinality with collapses
论文作者
论文摘要
{\ em单数基本假设}（SCH）是集合理论中最古典的组合原理之一。它说，如果$κ$是奇异的强限，则$ 2^κ=κ^+$。我们证明，鉴于地面模型中的奇异红衣主教$κ$为{\ em cofinality} $η$，这是合适的大型红衣主教的限制，$η^+= \aleph_γ$，然后有一个强迫延伸，然后保留了$κ$的$κ$，包括$κ$ n $ n $ the $ the $ the $ the $ thef。 $κ$。 此外，如果$η$不是$ \ aleph $固定点，则在我们的型号中，SCH以$ \aleph_η$失败。我们的大型基本假设低于木质枢机主教的存在。在我们的模型中，我们还获得了一个很好的规模。
The {\em Singular Cardinal Hypothesis} (SCH) is one of the most classical combinatorial principles in set theory. It says that if $κ$ is singular strong limit, then $2^κ=κ^+$. We prove that given a singular cardinal $κ$ of {\em cofinality} $η$ in the ground model, which is a limit of suitable large cardinals, and $η^+=\aleph_γ$, then there is a forcing extension which preserves cardinals and cofinalities up to and including $η$, such that $κ$ becomes $\aleph_{γ+η}$, and SCH fails at $κ$. Furthermore, if $η$ is not an $\aleph$-fixed point, then in our model, SCH fails at $\aleph_η$. Our large cardinal assumption is below the existence of a Woodin cardinal. In our model we also obtain a very good scale.
