|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||ABSOLUTENESS FOR UNIVERSALLY BAIRE SETS AND THE UNCOUNTABLE II||Journal:||Computational Prospects of Infinity Part II : Presented Talks||Volume:||15||First page:||163||Last page:||192||Issue Date:||2008||ISBN:||978-981-279-654-7||DOI:||10.1142/9789812796554_0009||Abstract:||
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 preventing one.
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