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arXiv · 2607.18726

Determining the Rearrangement Number

Vinicius de Oliveira Rodrigues
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Abstract

The rearrangement number $\mathfrak{rr}$ is the least cardinality of a collection of permutations of $\omega$ 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 $\mathfrak{rr}=\operatorname{non}(\mathcal M)$.

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Vinicius de Oliveira Rodrigues. 2026-07-21. Determining the Rearrangement Number. https://arxiv.org/abs/2607.18726

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