A game for Baire’s grand theorem

A game for Baire’s grand theorem

Generalizing a result of Kiss, we provide a game that characterizes Baire class 1 1 functions between arbitrary separable metrizable spaces. We show that the determinacy of our game is equivalent to a generalization of Baire’s grand theorem, and that both these statements hold under A D \mathsf {AD}...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2024-11, Vol.152 (11), p.4903-4914
1. Verfasser: Notaro, Lorenzo
Format: Artikel
Sprache:eng
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Zusammenfassung:Generalizing a result of Kiss, we provide a game that characterizes Baire class 1 1 functions between arbitrary separable metrizable spaces. We show that the determinacy of our game is equivalent to a generalization of Baire’s grand theorem, and that both these statements hold under A D \mathsf {AD} and in Solovay’s model.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/17025