We show that a comeager Π₁¹ hereditary family of compact sets must have a dense subfamily which is also hereditary. Using this, we prove an “abstract” result which implies the existence of independent ℳ ₀-sets, the meagerness of ₀-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true sets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-2-1,
author = {\'Etienne Matheron and Miroslav Zelen\'y},
title = {Rudin-like sets and hereditary families of compact sets},
journal = {Fundamenta Mathematicae},
volume = {185},
year = {2005},
pages = {97-116},
zbl = {1077.03028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-2-1}
}
Étienne Matheron; Miroslav Zelený. Rudin-like sets and hereditary families of compact sets. Fundamenta Mathematicae, Tome 185 (2005) pp. 97-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm185-2-1/