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Mad Families Constructed from Perfect Almost Disjoint Families

  • Jörg Brendle (a1) and Yurii Khomskii (a2)

Abstract

We prove the consistency of together with the existence of a -definable mad family, answering a question posed by Friedman and Zdomskyy in [7, Question 16]. For the proof we construct a mad family in L which is an ℵ1-union of perfect a.d. sets, such that this union remains mad in the iterated Hechler extension. The construction also leads us to isolate a new cardinal invariant, the Borel almost-disjointness number , defined as the least number of Borel a.d. sets whose union is a mad family. Our proof yields the consistency of (and hence, ).

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Mad Families Constructed from Perfect Almost Disjoint Families

  • Jörg Brendle (a1) and Yurii Khomskii (a2)

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