Models in which every nonmeager set is nonmeager in a nowhere dense Cantor set
Maxim R. Burke, Arnold W. Miller
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 intersect C is nonmeager in C. We also examine variants of this result and establish a measure theoretic analog.
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