How can we recognize potentially ${\bf\Pi}^0_\xi$ subsets of the plane?

Dominique Lecomte (1)

1 IMJ - Institut de Mathématiques de Jussieu

Let $\xi\geq 1$ be a countable ordinal. We study the Borel subsets of the plane that can be made ${\bf\Pi}^0_\xi$ by refining the Polish topology on the real line. These sets are called potentially ${\bf\Pi}^0_\xi$. We give a Hurewicz-like test to recognize potentially ${\bf\Pi}^0_\xi$ sets.

Mots clés: Potentially; Baire classes; Reduction; Hurewicz's Theorem

Domaines: Logique [math.LO]; Catégories et ensembles [math.CT]; Topologie générale [math.GN]

Dominique Lecomte. How can we recognize potentially ${\bf\Pi}^0_\xi$ subsets of the plane?. 2006. ⟨hal-00389795⟩