Uniformisations partielles et crit\`eres \`a la Hurewicz dans le plan

TL;DR

This paper characterizes certain Borel sets with countable sections in Polish spaces using partial uniformization, linking their potential classification in Wadge hierarchy.

Contribution

It provides new characterizations of Borel sets with countable sections via partial uniformization within the Wadge hierarchy framework.

Findings

Characterization of Borel sets potentially in Wadge classes

Use of partial uniformization results

Insights into the structure of Borel sets with countable sections

Abstract

We give characterizations of the Borel sets potentially in some Wadge class, among the Borel sets with countable vertical sections of a product of two Polish spaces. To do this, we use some partial uniformization results.