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1. CJM 2005 (vol 57 pp. 1139)
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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 forcing Categories:03E35, 03E17, 03E50 |