Year: 2026
Type: preprint
Abstract: 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 $\mathfrak{rr}=\operatorname{non}(\mathcal M)$.
Source: arXiv (Cornell University)
Author: Rodrigues, Vinicius de Oliveira
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170033442