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Models in Which Every Nonmeager Set is Nonmeager in a Nowhere Dense Cantor Set |
Canad. J. Math. 57(2005), 1139-1154
Published:2005-12-01
Printed: Dec 2005
Printed: Dec 2005
- 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 $A\cap C$ 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 |
| MSC Classifications: |
03E35 - Consistency and independence results 03E17 - Cardinal characteristics of the continuum 03E50 - Continuum hypothesis and Martin's axiom [See also 03E57] |