How to drive our families mad

Fuchino, Sakae and Geschke, Stefan and Soukup, Lajos (2011) How to drive our families mad. Arch. Math. Logic . (In Press)

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Abstract

Given a family of pairwise almost disjoint (ad) sets on a countable set , we study families of maximal almost disjoint (mad) sets extending .
We define to be the minimal possible cardinality of for such and . We show that all infinite cardinals less than or equal to the continuum can be represented as for some ad and that the inequalities and are both consistent.
We also give several constructions of mad families with some additional properties.

Item Type: Article cardinal invariants, almost disjoint number, Cohen model, destructible maximal almost disjoint family 03E35 Consistency and independence results Research Divisions > Set theory and general topology 10 Jan 2011 16:07

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