Models in which every nonmeager set is nonmeager in a nowhere dense Cantor set

2003/11/25 by Maxim R. Burke, Burke, Maxim R., Arnold W. Miller +1
Mathematics · #03E35 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E35

paper · pdf · doi:10.48550/arxiv.math/0311443

LaTex2e, 12 pages

arxiv created 2003/11/25 · arxiv updated 2009/12/01

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 intersect C is nonmeager in C. We also examine variants of this result and establish a measure theoretic analog.

Related

• Strongly meager sets can be quite big
• Universally meager sets in the Miller model and similar ones
• Excursions on Cantor-like Sets
• A tame Cantor set
• An non-centered asymmetric Cantor-like Set