论文标题
大心电等级结构中结构反射的模式
Patterns of Structural Reflection in the large-cardinal hierarchy
论文作者
论文摘要
我们在第一个可衡量的基本主教以下的大心电层次结构中揭示了结构反射的新模式。也就是说，我们从结构反射原理的弱形式以及弱产物的结构反射方面给出了两种不同的表征和微妙的红衣主教。我们的分析提示了$ c^{（n）} $的新概念的引入 - 对于每个自然数量$ n $，都可以展开的红衣主教，我们表明这些红衣主教形成了与$ c^{（n）$ - 扩展的$ c^{（n）} $ - extendible和$ niepalible和$ cardinals unifors of poctable fromble-fromable and cartinals类似的天然等级。这些结果表明，在第一个强烈展开和第一个微妙的红衣主教之间组成的大心态层次结构相对较低的区域完全类似于第一强与第一个伍德丁红衣主教之间更高的区域，也与第一个超级竞争和第一个vopcrical和第一个vopěnkanka nka nka nka nka nka nka Cardinals之间的层次结构相比。
We unveil new patterns of Structural Reflection in the large-cardinal hierarchy below the first measurable cardinal. Namely, we give two different characterizations of strongly unfoldable and subtle cardinals in terms of a weak form of the principle of Structural Reflection, and also in terms of weak product structural reflection. Our analysis prompts the introduction of the new notion of $C^{(n)}$-strongly unfoldable cardinal for every natural number $n$, and we show that these cardinals form a natural hierarchy between strong unfoldable and subtle cardinals analogous to the known hierarchies of $C^{(n)}$-extendible and $Σ_n$-strong cardinals. These results show that the relatively low region of the large-cardinal hierarchy comprised between the first strongly unfoldable and the first subtle cardinals is completely analogous to the much higher region between the first strong and the first Woodin cardinals, and also to the much further upper region of the hierarchy ranging between the first supercompact and the first Vopěnka cardinals.
