A MAD Q-set
Volume 178 / 2003
Fundamenta Mathematicae 178 (2003), 271-281
MSC: Primary 03E35.
DOI: 10.4064/fm178-3-6
Abstract
A MAD (maximal almost disjoint) family is an infinite subset ${\mathcal A}$ of the infinite subsets of $\omega =\{0,1,2,\ldots\}$ such that any two elements of ${\mathcal A}$ intersect in a finite set and every infinite subset of $\omega $ meets some element of ${\mathcal A}$ in an infinite set. A Q-set is an uncountable set of reals such that every subset is a relative $G_\delta $-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 $P(\omega )=2^{\omega }$.
