Models in which every nonmeager set is nonmeager in ...

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Title Models in which every nonmeager set is nonmeager in a nowhere dense Cantor set
Author(s) Maxim R. Burke, A. W. Miller
Journal Canadian Journal of Mathematics / Journal Canadien De Mathematiques
Date 2005
Volume 57
Issue 6
Start page 1139
End page 1154
Abstract We prove that it is relatively consistent with ZFC that in any perfect Polish space, for every nonmeager set A there exists a nowhere dense Cantor set C such that A boolean AND C is nonmeager in C. We also examine variants of this result and establish a measure theoretic analog.

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