Non-Collapse of the Effective Wadge Hierarchy

TL;DR

This paper investigates the effective Wadge hierarchy in effective spaces, providing conditions for its non-collapse and exploring hierarchies of sets and partitions with concrete applications.

Contribution

It establishes sufficient conditions for the non-collapse of the effective Wadge hierarchy and applies these to specific effective spaces, also studying hierarchies of k-partitions.

Findings

Identified conditions preventing hierarchy collapse.

Applied conditions to concrete effective spaces.

Analyzed hierarchies of sets and k-partitions.

Abstract

We study the recently suggested effective Wadge hierarchy in effective spaces, concentrating on the non-collapse property. Along with hierarchies of sets, we study hierarchies of $k$-partitions which are interesting on their own. In particular, we establish sufficient conditions for the non-collapse of the effective Wadge hierarchy and apply them to some concrete spaces.