Madness and (weak) normality

César Corral

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arXiv · 2101.01829

Madness and (weak) normality

César Corral

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Abstract

We consider weakenings of normality in $\Psi$-spaces and prove that the existence of a MAD family whose $\Psi$-space is almost-normal is independent of \textsf{ZFC}. We also construct a partly-normal not quasi-normal AD family, answering questions from Garc\'ia-Balan and Szeptycki. We finish by showing that the concepts of almost-normal and strongly $\aleph_0$-separated AD families are different, even under \textsf{CH}, answering a question from Oliveira-Rodrigues and Santos-Ronchim

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César Corral. 2021-01-06. Madness and (weak) normality. https://arxiv.org/abs/2101.01829

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