Hugo Nobrega ; Arno Pauly - Game characterizations and lower cones in the Weihrauch degrees

lmcs:4284 - Logical Methods in Computer Science, August 6, 2019, Volume 15, Issue 3 -
Game characterizations and lower cones in the Weihrauch degrees

Authors: Hugo Nobrega ; Arno Pauly

We introduce a parametrized version of the Wadge game for functions and show that each lower cone in the Weihrauch degrees is characterized by such a game. These parametrized Wadge games subsume the original Wadge game, the eraser and backtrack games as well as Semmes's tree games. In particular, we propose that the lower cones in the Weihrauch degrees are the answer to Andretta's question on which classes of functions admit game characterizations. We then discuss some applications of such parametrized Wadge games. Using machinery from Weihrauch reducibility theory, we introduce games characterizing every (transfinite) level of the Baire hierarchy via an iteration of a pruning derivative on countably branching trees.

Volume: Volume 15, Issue 3
Published on: August 6, 2019
Accepted on: August 6, 2019
Submitted on: February 15, 2018
Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science,03E15, 54H05, 03D60, 03F15


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