On ⅁ Γ \Game \mathbf {\Gamma } -complete sets

On ⅁ Γ \Game \mathbf {\Gamma } -complete sets

Extending a result of A. Kechris we prove that under suitable assumptions on the class Γ\mathbf {\Gamma } of Borel sets, in particular when Γ\mathbf {\Gamma } is a Baire class, if any ⅁Γ\Game \mathbf {\Gamma } set is reducible to some ⅁Γ\Game \mathbf {\Gamma } set AA by a ⅁Γ\Game \mathbf {\Gamma }-m...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2019-08, Vol.148 (2), p.859-873
Hauptverfasser: Debs, Gabriel, Saint Raymond, Jean
Format: Artikel
Sprache:eng
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Research article
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Zusammenfassung:Extending a result of A. Kechris we prove that under suitable assumptions on the class Γ\mathbf {\Gamma } of Borel sets, in particular when Γ\mathbf {\Gamma } is a Baire class, if any ⅁Γ\Game \mathbf {\Gamma } set is reducible to some ⅁Γ\Game \mathbf {\Gamma } set AA by a ⅁Γ\Game \mathbf {\Gamma }-measurable function, then AA is ⅁Γ\Game \mathbf {\Gamma }-complete.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14731