Hurewicz-like tests for Borel subsets of the plane

Dominique Lecomte (1)

1 IMJ - Institut de Mathématiques de Jussieu

Let xi be a non-null countable ordinal. We study the Borel subsets of the plane that can be made $\bormxi$ by refining the Polish topology on the real line. These sets are called potentially $\bormxi$. We give a Hurewicz-like test to recognize potentially $\bormxi$ sets.

Mots clés: potentially; Baire classes; reduction; Hurewicz's Theorem

Domaines: Logique [math.LO]; Topologie générale [math.GN]

Dominique Lecomte. Hurewicz-like tests for Borel subsets of the plane. Electronic Research Announcements of the American Mathematical Society, 2005, 11, pp.95-102. ⟨hal-00175695⟩