Absoluteness for Universally Baire Sets and the Uncountable Ii
نویسندگان
چکیده
Using ♦ and large cardinals we extend results of Magidor–Malitz and Farah–Larson to obtain models correct for the existence of uncountable homogeneous sets for finite-dimensional partitions and universally Baire sets. Furthermore, we show that the constructions in this paper and its predecessor can be modified to produce a family of 2ω1 -many such models so that no two have a stationary, costationary subset of ω1 in common. Finally, we extend a result of Steel to show that trees on reals of height ω1 which are coded by universally Baire sets have either an uncountable path or an absolute impediment
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