Geodesic
A MAD Q-set
Arnold W. Miller1
1 Department of Mathematics, Van Vleck Hall University of Wisconsin-Madison 480 Lincoln Drive Madison, WI 53706-1388, U.S.A.
Fundamenta Mathematicae, Tome 178 (2003) no. 3, pp. 271-281.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $P(\omega )=2^{\omega }$.
DOI : 10.4064/fm178-3-6
Mots-clés : mad maximal almost disjoint family infinite subset mathcal infinite subsets omega ldots elements mathcal intersect finite set every infinite subset omega meets element mathcal infinite set q set uncountable set reals every subset relative delta set shown relatively consistent zfc there exists mad family which q set topology inherits subset omega omega

Arnold W. Miller 1

1 Department of Mathematics, Van Vleck Hall University of Wisconsin-Madison 480 Lincoln Drive Madison, WI 53706-1388, U.S.A. 
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Arnold W. Miller. A MAD Q-set. Fundamenta Mathematicae, Tome 178 (2003) no. 3, pp. 271-281. doi : 10.4064/fm178-3-6. https://geodesic-test.mathdoc.fr/articles/10.4064/fm178-3-6/

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