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1. CJM 2005 (vol 57 pp. 1139)

Burke, Maxim R.; Miller, Arnold W.
 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

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