English

Continuum Many Different Things: Localisation, Anti-Localisation and Yorioka Ideals

Logic 2024-05-06 v4

Abstract

Combining creature forcing approaches from arXiv:1003.3425 and arXiv:1402.0367, we show that, under CH, there is a proper ωω\omega^\omega-bounding poset with 2\aleph_2-cc that forces continuum many pairwise different cardinal characteristics, parametrised by reals, for each one of the following six types: uniformity and covering numbers of Yorioka ideals as well as both kinds of localisation and anti-localisation cardinals, respectively. This answers several open questions from arXiv:1805.11005.

Keywords

Cite

@article{arxiv.2110.11614,
  title  = {Continuum Many Different Things: Localisation, Anti-Localisation and Yorioka Ideals},
  author = {Miguel Antonio Cardona and Lukas Daniel Klausner and Diego Alejandro Mejía},
  journal= {arXiv preprint arXiv:2110.11614},
  year   = {2024}
}

Comments

65 pages, 6 figures