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

Published online by Cambridge University Press:  20 November 2018

Maxim R. Burke  and
Arnold W. Miller
Maxim R. Burke
Affiliation:
Department of Mathematics and Statistics, University of Prince Edward Island, Charlottetown, Prince Edward Island, C1A 4P3, email: burke@upei.ca
Arnold W. Miller
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388, USA, email: miller@math.wisc.edu website: http://www.math.wisc.edu/∽miller
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Abstract

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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

Primary: 03E35secondary: 03E1703E50Property of BaireLebesgue measureCantor setoracle forcing
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 6 , 01 December 2005 , pp. 1139 - 1154
Copyright
Copyright © Canadian Mathematical Society 2005

References

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