English

Cicho\'n's maximum with evasion number

Logic 2025-07-02 v2

Abstract

We show that the evasion number e\mathfrak{e} can be added to Cicho\'n's maximum with a distinct value. More specifically, it is consistent that 1<add(N)<cov(N)<b<e<non(M)<cov(M)<d<non(N)<cof(N)<20\aleph_1<\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{b}<\mathfrak{e}<\mathrm{non}(\mathcal{M})<\mathrm{cov}(\mathcal{M})<\mathfrak{d}<\mathrm{non}(\mathcal{N})<\mathrm{cof}(\mathcal{N})<2^{\aleph_0} holds.

Cite

@article{arxiv.2401.14600,
  title  = {Cicho\'n's maximum with evasion number},
  author = {Takashi Yamazoe},
  journal= {arXiv preprint arXiv:2401.14600},
  year   = {2025}
}

Comments

33pages,11figures

R2 v1 2026-06-28T14:27:43.392Z