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Game characterizations and lower cones in the Weihrauch degrees

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We introduce generalized Wadge games and show that each lower cone in the Weihrauch degrees is characterized by such a game. These generalized Wadge games subsume the original Wadge games, the eraser and backtrack games as well as variants of Semmes' tree games. As a new example we introduce the tree derivative games which characterize all even finite levels of the Baire hierarchy, and a variant characterizing the odd finite levels.


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