English

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

Logic 2009-06-01 v1 Category Theory General Topology

Abstract

Let ξ1\xi\geq 1 be a countable ordinal. We study the Borel subsets of the plane that can be made Πξ0{\bf\Pi}^0_\xi by refining the Polish topology on the real line. These sets are called potentially Πξ0{\bf\Pi}^0_\xi. We give a Hurewicz-like test to recognize potentially Πξ0{\bf\Pi}^0_\xi sets.

Keywords

Cite

@article{arxiv.0905.4875,
  title  = {How can we recognize potentially ${\bf\Pi}^0_\xi$ subsets of the plane?},
  author = {Dominique Lecomte},
  journal= {arXiv preprint arXiv:0905.4875},
  year   = {2009}
}
R2 v1 2026-06-21T13:07:37.649Z