Lipschitz and uniformly continuous reducibilities on ultrametric Polish spaces

TL;DR

This paper investigates the structure of reducibilities induced by various classes of functions on ultrametric Polish spaces, examining their properties under different set-theoretical assumptions.

Contribution

It provides a detailed analysis of the degree-structures formed by these reducibilities and assesses their well-behavedness in different set-theoretic contexts.

Findings

Degree-structures vary with the class of functions considered.

Under certain assumptions, these structures are well-behaved.

The analysis applies to arbitrary ultrametric Polish spaces.

Abstract

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.