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

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

2009-05-29

arxiv.org/abs/0905.4875v1

Mathematics

Logic

Scientific paper

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.

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