Lipschitz and uniformly continuous reducibilities on ultrametric Polish spaces

We analyze the reducibilities induced by, respectively, uniformly continuous, Lipschitz, and nonexpansive functions on arbitrary ultrametric Polish spaces, and determine whether under suitable set-theoretical assumptions the induced degree-structures are well-behaved.Comment: 37 pages, 2 figures, revised version, accepted for publication in the Festschrift that will be published on the occasion of Victor Selivanov's 60th birthday by Ontos-Verlag. A mistake has been corrected in Section

Unveiling Dynamics and Complexity

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 (a variant of) 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 generalized Wadge games.SCOPUS: cp.kinfo:eu-repo/semantics/publishe

Game characterizations and lower cones in the Weihrauch degrees

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