Geodesic
Special sets of reals and weak forms of normality on Isbell--Mrówka spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 109-126.

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We recall some classical results relating normality and some natural weakenings of normality in $\Psi$-spaces over almost disjoint families of branches in the Cantor tree to special sets of reals like $Q$-sets, $\lambda$-sets and $\sigma$-sets. We introduce a new class of special sets of reals which corresponds to the corresponding almost disjoint family of branches being $\aleph_0$-separated. This new class fits between $\lambda$-sets and perfectly meager sets. We also discuss conditions for an almost disjoint family $\mathcal A$ being potentially almost-normal (pseudonormal), in the sense that $\mathcal A$ is almost-normal (pseudonormal) in some c.c.c. forcing extension.
DOI : 10.14712/1213-7243.2023.014
Classification : 54D15, 54D80
Keywords: Isbell--Mrówka spaces; almost disjoint families; almost-normal; weak $\lambda$-set 
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de Oliveira Rodrigues, Vinicius; dos Santos Ronchim, Victor; Szeptycki, Paul J. Special sets of reals and weak forms of normality on Isbell--Mrówka spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 109-126. doi : 10.14712/1213-7243.2023.014. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.014/

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