Baire-class ξ colorings: the first three levels

نویسندگان

  • Dominique LECOMTE
  • Miroslav ZELENY
چکیده

The G0-dichotomy due to Kechris, Solecki and Todorčević characterizes the analytic relations having a Borel-measurable countable coloring. We give a version of the G0-dichotomy for Σ 0 ξ-measurable countable colorings when ξ ≤ 3. A Σ 0 ξ-measurable countable coloring gives a covering of the diagonal consisting of countably many Σξ squares. This leads to the study of countable unions of Σξ rectangles. We also give a Hurewicz-like dichotomy for such countable unions when ξ≤2. 2010 Mathematics Subject Classification. Primary: 03E15, Secondary: 54H05

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تاریخ انتشار 2011