A MAD (maximal almost disjoint) family is an infinite subset of the infinite subsets of ω = 0,1,2,... such that any two elements of intersect in a finite set and every infinite subset of ω meets some element of in an infinite set. A Q-set is an uncountable set of reals such that every subset is a relative -set. It is shown that it is relatively consistent with ZFC that there exists a MAD family which is also a Q-set in the topology it inherits as a subset of .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-3-6,
author = {Arnold W. Miller},
title = {A MAD Q-set},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {271-281},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-3-6}
}
Arnold W. Miller. A MAD Q-set. Fundamenta Mathematicae, Tome 177 (2003) pp. 271-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-3-6/