PreprintCC BY 4.0arXiv
Almost Disjointness Principles and Q-Space Cardinals
Abstract
Banakh and Bazylevych introduced separation-axiom variants qi, for i=1,2,21/2, of the cardinal q, together with a cardinal adp lying between dp and ap. They asked whether adp coincides with either of these two cardinals. We prove in ZFC that adp=dp. We define a dual variant adp2 and show that adp2=ap. We further study the relation between ap and the weakened Q-space cardinals. We introduce a tree analogue at of ap and prove at=q2, concluding that ap≤q2, which answers a question of Banakh and Bazylevych. Assuming the Generalized Continuum Hypothesis, we construct ccc forcing extensions with ap=ω1<at=c, so ap<q2 is consistent with ZFC.
Related
- Almost simple subgroups of the space Cremona group
- On disjointness of 3-IETs from mixing and lightly mixing systems
- Jónsson cardinals, Magidor cardinals, and the number of omitted colors
- On disjointness and ℱ-product recurrence with respect to zero entropy systems
- Identity crisis on tightly C(2)-compact cardinals
BibTeX
@misc{rodrigues2026almost,
title = {{Almost Disjointness Principles and $Q$-Space Cardinals}},
author = {Vinicius de Oliveira Rodrigues},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.11326},
eprint = {2605.11326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.11326},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Almost Disjointness Principles and Q-Space Cardinals
AU - Vinicius de Oliveira Rodrigues
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2605.11326
UR - https://arxiv.org/abs/2605.11326
AB - Banakh and Bazylevych introduced separation-axiom variants q_i, for i=1,2,21/2, of the cardinal q, together with a cardinal adp lying between dp and ap. They asked whether adp coincides with either of these two cardinals. We prove in ZFC that adp=dp. We define a dual variant adp_2 and show that adp_2=ap. We further study the relation between ap and the weakened Q-space cardinals. We introduce a tree analogue at of ap and prove at=q_2, concluding that ap≤q_2, which answers a question of Banakh and Bazylevych. Assuming the Generalized Continuum Hypothesis, we construct ccc forcing extensions with ap=ω_1<at=c, so ap<q_2 is consistent with ZFC.
ER -