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Models in Which Every Nonmeager Set is Nonmeager in a Nowhere Dense Cantor Set

  Published:2005-12-01
 Printed: Dec 2005
  • Maxim R. Burke
  • Arnold W. Miller
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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 Property of Baire, Lebesgue measure, Cantor set, oracle forcing
MSC Classifications: 03E35, 03E17, 03E50 show english descriptions Consistency and independence results
Cardinal characteristics of the continuum
Continuum hypothesis and Martin's axiom [See also 03E57]
03E35 - Consistency and independence results
03E17 - Cardinal characteristics of the continuum
03E50 - Continuum hypothesis and Martin's axiom [See also 03E57]
 

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