标题： 更广泛系统的更高极限 显示英文标题

标题： Higher limits of wider systems

摘要： 将$\mathbf{A}_\lambda$写为可能被描述为由从基数$\lambda$到自然数集合的函数索引的最基础的非平凡逆系统。 对于任何固定的$n$，导出极限$\mathrm{lim}^n\,\mathbf{A}_\lambda$是否仅在无限基数$\lambda$的类的一个非空子集上消失的问题，在 [Be17] 和 [Ban23] 中均有记录，并与几个相关的进一步问题密切相关。 我们对此问题给出了肯定回答；事实上，我们证明了最大可能性，即这种情况可以在每个度数$n>1$同时发生。 显示英文摘要

摘要： Write $\mathbf{A}_\lambda$ for what might be described as the most elementary nontrivial inverse system of abelian groups indexed by the functions from the cardinal $\lambda$ to the set of natural numbers. The question of whether for any fixed $n$ the derived limit $\mathrm{lim}^n\,\mathbf{A}_\lambda$ may vanish for only a nonempty subset of the class of infinite cardinals $\lambda$ is recorded in both [Be17] and [Ban23], and bears closely on several related further ones. We answer this question in the affirmative; in fact, we show the maximal possibility, namely that this can simultaneously happen in every degree $n>1$.