Dominique Lecomte
Published 2010-02-07Version 1
Let $\bf\Gamma$ be a Borel class, or a Wadge class of Borel sets, and $2\leq d\leq\omega$ a cardinal. We study the Borel subsets of ${\mathbb R}^d$ that can be made $\bf\Gamma$ by refining the Polish topology on the real line. These sets are called potentially $\bf\Gamma$. We give a test to recognize potentially $\bf\Gamma$ sets.
How can we recognize potentially ${\bfΠ}^0_ξ$ subsets of the plane?
Decomposing the real line into Borel sets closed under addition
Hurewicz-like tests for Borel subsets of the plane
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