## Vinicius de Oliveira Rodrigues, Victor dos Santos Ronchim, Paul J. Szeptycki

*Special sets of reals and weak forms of normality on Isbell-Mrówka spaces*

Comment.Math.Univ.Carolin. 64,1 (2023) 109-126.**Abstract: **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.

**Keywords:** Isbell-Mrówka spaces; almost disjoint families; almost-normal; weak \lambda-set

**DOI:** DOI 10.14712/1213-7243.2023.014

**AMS Subject Classification:** 54D15 54D80

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