论文标题
坚不可摧和反射
Weak Indestructibility and Reflection
论文作者
论文摘要
这项工作是我即将发表论文的一部分[7]。我们在（1）（1）在适当类强的枢机主教的情况下，（1）所有$κ+2 $ 2 $ 2 $的强度之间的坚不可摧的不可能差异，（2）一类适当的红衣主教反映强者。实际上，我们的强度程度的坚不可摧弱，远远超出了$κ+2 $，远远超出了下一个无法访问的可测量极限（地面模型）。一个方向是使用强迫证明的，另一个使用内部模型理论的核心模型技术证明了方向。此外，讨论了坚不可摧的弱坚不可分性与与木质枢机主教相关的反射特性之间的联系。
This work is a part of my upcoming thesis [7]. We establish an equiconsistency between (1) weak indestructibility for all $κ+2$-degrees of strength for cardinals $κ$ in the presence of a proper class of strong cardinals, and (2) a proper class of cardinals that are strong reflecting strongs. We in fact get weak indestructibility for degrees of strength far beyond $κ+2$, well beyond the next inaccessible limit of measurables (of the ground model). One direction is proven using forcing and the other using core model techniques from inner model theory. Additionally, connections between weak indestructibility and the reflection properties associated with Woodin cardinals are discussed.
