Universally Baire sets in 2^κ

2024/12/21 by Ikegami, Daisuke, Viale, Matteo
#03E55 (Secondary) #03E57 (Primary) 03E15 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2412.16546

Abstract

We generalize the basic theory of universally Baire sets of 2^ω to a theory of universally Baire subsets of 2^κ. We show that the fundamental characterizations of the property of being universally Baire have natural generalizations that can be formulated also for subsets of 2^κ, in particular we provide four equivalent uniform definitions in the parameter κ (for κ an infinite cardinal) characterizing for each such κ the class of universally Baire subsets of 2^κ. For κ=ω, these definitions bring us back to the original notion of universally Baire sets of reals given by Feng, Magidor and Woodin [2].

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