Models in which every nonmeager set is nonmeager in a nowhere dense Cantor set
Burke, Maxim R.Miller, A. W.
Canadian Journal of Mathematics / Journal Canadien De Mathematiques
Mathematics and Statistics
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.