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

Miguel Antonio Cardona, Lukas Daniel Klausner, Diego Alejandro Mejía

Published 2021-10-22, updated 2022-01-20Version 2

Combining creature forcing approaches from arXiv:1003.3425 and arXiv:1402.0367, we show that, under CH, there is a proper $\omega^\omega$-bounding poset with $\aleph_2$-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.