English

Cicho\'n's maximum with cardinals of the closed null ideal

Logic 2025-07-02 v2

Abstract

Let E\mathcal{E} denote the σ\sigma-ideal generated by closed null sets on the reals. We show that the uniformity and the covering of E\mathcal{E} can be added to Cicho\'n's maximum with distinct values. More specifically, it is consistent that 1<add(N)<cov(N)<b<non(E)<non(M)<cov(M)<cov(E)<d<non(N)<cof(N)<20\aleph_1<\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{b}<\mathrm{non}(\mathcal{E})<\mathrm{non}(\mathcal{M})<\mathrm{cov}(\mathcal{M})<\mathrm{cov}(\mathcal{E})<\mathfrak{d}<\mathrm{non}(\mathcal{N})<\mathrm{cof}(\mathcal{N})<2^{\aleph_0} holds.

Keywords

Cite

@article{arxiv.2412.09069,
  title  = {Cicho\'n's maximum with cardinals of the closed null ideal},
  author = {Takashi Yamazoe},
  journal= {arXiv preprint arXiv:2412.09069},
  year   = {2025}
}

Comments

34 pages, 6 figures