The motivation of this work goes back to the G0-dichotomy concerning countable Borel colorings, as well as the related result concerning the separation of disjoint analytic sets by a countable union of Borel rectangles. Lecomte and Zeleny proved level by level versions of these results, for the first three (respectively two) levels of the Borel hierarchy. We present here a new approach for Baire class two colorings, involving the representation of Borel sets initiated by Debs and Saint Raymond, by strengthening this representation for any Pi03 set. A strong use of effective topologies is made. This is joint work with Greenberg, Turetsky and Zeleny.