Rudin-like sets and hereditary families of compact sets
Volume 185 / 2005
Fundamenta Mathematicae 185 (2005), 97-116
MSC: 03E15, 28A05, 43A46.
DOI: 10.4064/fm185-2-1
Abstract
We show that a comeager ${\bf \Pi }_1^1$ hereditary family of compact sets must have a dense $G_\delta $ subfamily which is also hereditary. Using this, we prove an “abstract” result which implies the existence of independent ${{\mathcal M}}_0$-sets, the meagerness of ${\mathcal U}_0$-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true $F_{\sigma \delta }$ sets.
