On filling families of finite subsets of the Cantor set

Details On filling families of finite subsets of the Cantor set On filling families of finite subsets of the Cantor set

2008-05-14

arxiv.org/abs/0805.2031v1

Mathematical Proceedings of the Cambridge Phil. Society 145 (2008), 165-175

Mathematics

Logic

14 pages, no figures. Mathematical Proceedings of the Cambridge Philosophical Society (to appear)

Scientific paper

Let $\ee>0$ and $\fff$ be a family of finite subsets of the Cantor set $\ccc$. Following D. H. Fremlin, we say that $\fff$ is $\ee$-filling over $\ccc$ if $\fff$ is hereditary and for every $F\subseteq\ccc$ finite there exists $G\subseteq F$ such that $G\in\fff$ and $|G|\geq\ee |F|$. We show that if $\fff$ is $\ee$-filling over $\ccc$ and $C$-measurable in $[\ccc]^{<\omega}$, then for every $P\subseteq\ccc$ perfect there exists $Q\subseteq P$ perfect with $[Q]^{<\omega}\subseteq\fff$. A similar result for weaker versions of density is also obtained.

Affiliated with

Also associated with

No associations

Rating

On filling families of finite subsets of the Cantor set does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On filling families of finite subsets of the Cantor set, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On filling families of finite subsets of the Cantor set will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-55719