发表机构
Einstein Institute of Mathematics, The Hebrew University of Jerusalem（耶路撒冷希伯来大学爱因斯坦数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在ZFC中证明阶梯立方体与四元组关系的失败条件，并利用奇妙理想建立后继基数上的正极化关系，同时否定连续基数上的此类理想存在。
AI 中文摘要
我们在$\text{ZFC}$中证明，当$\text{λ}$为不可数基数时，$\text{λ}$-阶梯立方体关系总是失败。对应的四元组阶梯关系对每个$\text{λ}$均失败。若$\text{λ}$为$\text{ℵ}_0$，则相关的阶梯关系的一致性强度至少为一个Woodin基数。我们从奇妙理想出发，在后继基数和双重后继基数上证明了正极化关系。然而，我们表明，不存在同时覆盖两个连续基数的此类理想。
英文摘要
We prove, in $\mathsf{ZFC}$, that the $λ$-terraced cube relation fails whenever $λ$ is an uncountable cardinal. The corresponding terraced relation for quadruples fails for every $λ$. If $λ$ is $\aleph_0$ then the pretinent terraced relation has consistency strength of at least one Woodin cardinal. We prove positive polarized relations at a successor and a double successor from wondrous ideals. We show, however, that there are no such ideals over two consecutive cardinals simultaneously.
