Authors: Farah, Ilijas 
Ketchersid, Richard
Larson, Paul
Magidor, Menachem
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.
Publisher: World Scientific

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