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Search: All articles in the CMB digital archive with keyword almost disjoint family

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1. CMB 2013 (vol 57 pp. 119)

Mildenberger, Heike; Raghavan, Dilip; Steprans, Juris
Splitting Families and Complete Separability
We answer a question from Raghavan and Steprāns by showing that $\mathfrak{s} = {\mathfrak{s}}_{\omega, \omega}$. Then we use this to construct a completely separable maximal almost disjoint family under $\mathfrak{s} \leq \mathfrak{a}$, partially answering a question of Shelah.

Keywords:maximal almost disjoint family, cardinal invariants
Categories:03E05, 03E17, 03E65

2. CMB 1999 (vol 42 pp. 13)

Brendle, Jörg
Dow's Principle and $Q$-Sets
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
Categories:03E05, 03E35, 54A35

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