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Computable analysis and games in descriptive set theory

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Mathematical, Foundational and Computational Aspects of the Higher Infinite

We report on ongoing work with Arno Pauly, showing how concepts from computable analysis can be used to shed light and uniformize certain games for classes of functions which have been studied in descriptive set theory, such as Wadge’s game for continuous functions, Duparc’s eraser game for Baire class 1 functions, and Semmes’ tree game for Borel functions.

As an application, for each finite n we obtain a game characterizing the Baire class n of functions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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