Models in Which Every Nonmeager Set is Nonmeager in a Nowhere Dense Cantor Set 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 $A\cap C$ is nonmeager in $C$. We also examine variants of this result and establish a measure theoretic analog. Keywords:Property of Baire, Lebesgue measure,, Cantor set, oracle forcingCategories:03E35, 03E17, 03E50