We show that ω₁-Universally Baire self-justifying systems are fully Universally Baire under the Weak Stationary Reflection Principle for Pairs. This involves analyzing the notion of a weakly captured set of reals, a weakening of the Universal Baire Property.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-3,
author = {Stuart Zoble},
title = {Stationary reflection and the universal Baire property},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {45-56},
zbl = {1097.03044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-3}
}
Stuart Zoble. Stationary reflection and the universal Baire property. Fundamenta Mathematicae, Tome 189 (2006) pp. 45-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-3/