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/