. . "RIV/00216208:11320/14:10284964" . . "[83FB487293A7]" . "1"^^ . "000333413900003" . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "2"^^ . . . . "BAIRE-CLASS xi COLORINGS: THE FIRST THREE LEVELS"@en . "0002-9947" . . "The G(0)-dichotomy due to Kechris, Solecki and Todorcevic characterizes the analytic relations having a Borel-measurable countable coloring. We give a version of the G(0)-dichotomy for Sigma(0)(xi)-measurable countable colorings when xi {= 3. A Sigma(0)(xi)-measurable countable coloring gives a covering of the diagonal consisting of countably many Sigma(0)(xi) squares. This leads to the study of countable unions of Sigma(0)(xi) rectangles. We also give a Hurewicz-like dichotomy for such countable unions when xi {= 2."@en . . . . "BAIRE-CLASS xi COLORINGS: THE FIRST THREE LEVELS" . . "5" . "366" . "RIV/00216208:11320/14:10284964!RIV15-MSM-11320___" . "The G(0)-dichotomy due to Kechris, Solecki and Todorcevic characterizes the analytic relations having a Borel-measurable countable coloring. We give a version of the G(0)-dichotomy for Sigma(0)(xi)-measurable countable colorings when xi {= 3. A Sigma(0)(xi)-measurable countable coloring gives a covering of the diagonal consisting of countably many Sigma(0)(xi) squares. This leads to the study of countable unions of Sigma(0)(xi) rectangles. We also give a Hurewicz-like dichotomy for such countable unions when xi {= 2." . "I, P(GA201/09/0067)" . . "11320" . . "4788" . "29"^^ . "BAIRE-CLASS xi COLORINGS: THE FIRST THREE LEVELS"@en . . "product; partition; Hurewicz; dichotomy; coloring; Borel class; Borel chromatic number"@en . . "BAIRE-CLASS xi COLORINGS: THE FIRST THREE LEVELS" . . "Zelen\u00FD, Miroslav" . "Lecomte, Dominique" . . . "Transactions of the American Mathematical Society" . .