Resumen de Hierarchies of [ ... ] º 2-measurable k -partitions

Victor L. Selivanov

• Attempts to extend the classical Hausdorff difference hierarchy to the case of partitions of a space to k > 2 subsets lead to non-equivalent notions. In a hope to identify the right extension we consider the extensions appeared in the literature so far: the limit-, level-, Boolean and Wadge hierarchies of k -partitions. The advantages and disadvantages of the four hierarchies are discussed. The main technical contribution of this paper is a complete characterization of the Wadge degrees of [ ¿ ] º 2-measurable k -partitions of the Baire space.