Classes de Wadge potentielles et th\'eor\`emes d'uniformisation partielle

TL;DR

The paper introduces potential Wadge classes and develops uniformization theorems for complex Borel sets in product Polish spaces, focusing on non-potentially closed sets and their properties.

Contribution

It proposes a simple construction for Borel subsets in product Polish spaces and explores potential Wadge classes and partial uniformization results.

Findings

Characterization of non-potentially closed sets

Hurewicz-like theorems for Borel sets

Partial uniformization results on large sets

Abstract

We want to give a construction as simple as possible of a Borel subset of a product of two Polish spaces. This introduces the notion of potential Wadge class. Among other things, we study the non-potentially closed sets, by proving Hurewicz-like results. This leads to partial uniformization theorems, on big sets, in the sense of cardinality or Baire category.