Mad families constructed from perfect almost disjoint families
نویسندگان
چکیده
We prove the consistency of b > א1 together with the existence of a Π11definable 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 aB , defined as the least number of Borel a.d. sets whose union is a mad family. Our proof yields the consistency of aB < b (and hence, aB < a). §
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ورودعنوان ژورنال:
- J. Symb. Log.
دوره 78 شماره
صفحات -
تاریخ انتشار 2013