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We construct a model of ZFC with a singular cardinal such that every subset of in L (V+₁) has both the -Perfect Set Property and the U-Baire Property. This is a higher analogue of Solovay's result for L (R). We obtain this configuration starting with large-cardinal assumptions in the realm of supercompactness, thus improving former theorems by Cramer, Shi and Woodin.
Dimonte et al. (Mon,) studied this question.