论文标题
无选的红衣主教和连续性问题
Choiceless cardinals and the continuum problem
论文作者
论文摘要
在库嫩不一致之外的大型主要假设下 - 假设是如此强烈以至于与选择的公理相矛盾 - 我们解决了广义连续性问题的几种变体，并确定了最终是定期定期的累积层次层级累积层次结构的级别$v_α$的结构特征。例如，如果从集合宇宙到本身的基本嵌入，那么对于足够大的序列$α$，在$v_α$上所有有良好关系的长度的至上是$v_α$的最高限制，并且只有$α$是奇数的，并且仅在$α$的情况下才是强的。
Under large cardinal hypotheses beyond the Kunen inconsistency -- hypotheses so strong as to contradict the Axiom of Choice -- we solve several variants of the generalized continuum problem and identify structural features of the levels $V_α$ of the cumulative hierarchy of sets that are eventually periodic, alternating according to the parity of the ordinal $α$. For example, if there is an elementary embedding from the universe of sets to itself, then for sufficiently large ordinals $α$, the supremum of the lengths of all wellfounded relations on $V_α$ is a strong limit cardinal if and only if $α$ is odd.
