How can we recognize potentially \bfΠ⁰_ξ subsets of the plane?

2009/05/29 by Dominique Lecomte, Lecomte, Dominique
Mathematics · #03E15 (Primary) #54H05 (Secondary) #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.CT #math.GN #math.LO #msc:03E15 #msc:54H05

paper · pdf · doi:10.48550/arxiv.0905.4875

arxiv created 2009/05/29 · arxiv updated 2009/12/01

Abstract

Let ξ≥ 1 be a countable ordinal. We study the Borel subsets of the plane that can be made \bfΠ⁰_ξ by refining the Polish topology on the real line. These sets are called potentially \bfΠ⁰_ξ. We give a Hurewicz-like test to recognize potentially \bfΠ⁰_ξ sets.

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