How can we recognize potentially ${\bfΠ}^0_ξ$ subsets of the plane?

Dominique Lecomte

Published 2009-05-29Version 1

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.