English

Con($\mathfrak{r}_{\mathsf{nwd}}<\mathfrak{irr}$)

Logic 2025-05-05 v1

Abstract

We prove the consistency of the inequality rnwd<irr\mathfrak{r}_{\mathsf{nwd}}<\mathfrak{irr}, which in turn implies the consistency of rnwd<i\mathfrak{r}_\mathsf{nwd}<\mathfrak{i} and rscatt<irr\mathfrak{r}_{\mathsf{scatt}}<\mathfrak{irr}. This answers one question from \cite{balzar_hrusak_hernandez} and one question from \cite{cancino_irresolvable_1}. We also prove the consistency of the inequality rQ<uQ\mathfrak{r}_\mathbb{Q}<\mathfrak{u}_\mathbb{Q}.

Cite

@article{arxiv.2505.01004,
  title  = {Con($\mathfrak{r}_{\mathsf{nwd}}<\mathfrak{irr}$)},
  author = {Jonathan Cancino Manríquez},
  journal= {arXiv preprint arXiv:2505.01004},
  year   = {2025}
}

Comments

19 pages

R2 v1 2026-06-28T23:18:48.917Z