Mathematics – Logic
Scientific paper
1996-10-25
Mathematics
Logic
Scientific paper
Larman showed that any closed subset of the plane with uncountable vertical cross-sections has aleph_1 disjoint Borel uniformizing sets. Here we show that Larman's result is best possible: there exist closed sets with uncountable cross-sections which do not have more than aleph_1 disjoint Borel uniformizations, even if the continuum is much larger than aleph_1. This negatively answers some questions of Mauldin. The proof is based on a result of Stern, stating that certain Borel sets cannot be written as a small union of low-level Borel sets. The proof of the latter result uses Steel's method of forcing with tagged trees; a full presentation of this method, written in terms of Baire category rather than forcing, is given here.
Becker Howard
Dougherty Randall
No associations
LandOfFree
On disjoint Borel uniformizations 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 disjoint Borel uniformizations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On disjoint Borel uniformizations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-209817