Wadge-like reducibilities on ultrametric Polish spaces

We analyze the reducibilities induced by, respectively, uniformly continuous, Lipschitz, and nonexpansive functions on arbitrary ultrametric Polish spaces, and give sufficient and necessary (topological) conditions on such spaces for the corresponding degree-structures being well-behaved. If time permits, we will also briefly discuss how suitable set-theoretic assumptions may influence the behavior of these hierarchies. This is joint work with P. Schlicht.