Definable maximal discrete sets in forcing extensions
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Let be a Σ11 binary relation, and recall that a set A is -discrete if no two elements of A are related by . We show that in the Sacks and Miller forcing extensions of L there is a Δ12 maximal -discrete set. We use this to answer in the negative the main question posed in  by showing that in the Sacks and Miller extensions there is a Π11 maximal orthogonal family ("mof") of Borel probability measures on Cantor space. A similar result is also obtained for Π11 mad families. By contrast, we show that if there is a Mathias real over L then there are no Σ12 mofs.
|Tidsskrift||Mathematical Research Letters|
|Status||Udgivet - 2018|