16,338 research outputs found
Sacks Forcing and the Shrink Wrapping Property
We consider a property stronger than the Sacks property, called the shrink
wrapping property, which holds between the ground model and each Sacks forcing
extension. Unlike the Sacks property, the shrink wrapping property does not
hold between the ground model and a Silver forcing extension. We also show an
application of the shrink wrapping property.Comment: 16 page
Definable maximal discrete sets in forcing extensions
Let be a binary relation, and recall that a set
is -discrete if no two elements of are related by .
We show that in the Sacks and Miller forcing extensions of there is a
maximal -discrete set. We use this to answer in the
negative the main question posed in [5] by showing that in the Sacks and Miller
extensions there is a maximal orthogonal family ("mof") of Borel
probability measures on Cantor space. A similar result is also obtained for
mad families. By contrast, we show that if there is a Mathias real
over then there are no mofs.Comment: 16 page
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