发表机构
University of São Paulo（圣保罗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明在ZFC下排列数rr小于non(M)是一致的，并探讨了排列数与子级数数、分裂数之间的关系。
AI 中文摘要
排列数rr是使得每一个条件收敛实数级数被某些排列破坏的最小基数集合的最小基数。Blass、Brendle、Brian、Hamkins、Hardy和Larson证明了max{cov(N),b}≤rr≤non(M)，并询问rr<non(M)是否一致。我们证明了在ZFC下rr<non(M)是一致的。我们还证明，在不同的强制扩展中，max{cov(N),b}<rr。我们进一步推导了子级数数s_sub和分裂数s的后果。
英文摘要
The rearrangement number $\mathfrak{rr}$ is the least cardinality of a collection of permutations of $ω$ such that every conditionally convergent real series is disrupted by some permutation in the collection. Blass, Brendle, Brian, Hamkins, Hardy, and Larson proved that $\max\{\operatorname{cov}(\mathcal N),\mathfrak b\}\leq\mathfrak{rr}\leq\operatorname{non}(\mathcal M)$ and asked whether $\mathfrak{rr}=\operatorname{non}(\mathcal M)$. We prove in ZFC that $\mathfrak{rr}=\operatorname{non}(\mathcal M)$.
Comments9 pages, 3 figures. New title; substantially rewritten. A serious error in the use of the Laver property invalidated the v1 claim that rr < non(M) is consistent. This version replaces that claim with a ZFC proof of the opposite conclusion: rr = non(M)
