Perfect set theorems
Volume 201 / 2008
Fundamenta Mathematicae 201 (2008), 179-195
MSC: 03E05, 03E15, 03E17.
DOI: 10.4064/fm201-2-6
Abstract
We study splitting, infinitely often equal (ioe) and refining families from the descriptive point of view, i.e. we try to characterize closed, Borel or analytic such families by proving perfect set theorems. We succeed for $G_\delta $ hereditary splitting families and for analytic countably ioe families. We construct several examples of small closed ioe and refining families.
