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# Dow's Principle and $Q$-Sets

Published:1999-03-01
Printed: Mar 1999
• Jörg Brendle
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## Abstract

A $Q$-set is a set of reals every subset of which is a relative $G_\delta$. We investigate the combinatorics of $Q$-sets and discuss a question of Miller and Zhou on the size $\qq$ of the smallest set of reals which is not a $Q$-set. We show in particular that various natural lower bounds for $\qq$ are consistently strictly smaller than $\qq$.
 Keywords: $Q$-set, cardinal invariants of the continuum, pseudointersection number, $\MA$($\sigma$-centered), Dow's principle, almost disjoint family, almost disjointness principle, iterated forcing
 MSC Classifications: 03E05 - Other combinatorial set theory 03E35 - Consistency and independence results 54A35 - Consistency and independence results [See also 03E35]

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