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

Mathematical Logic Quarterly 53 (4):446-461 (2007)
Abstract
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
Keywords Boolean hierarchy of k ‐partitions  limit‐hierarchy  Difference hierarchy  Wadge reducibility  level‐hierarchy  homomorphic preorder
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DOI 10.1002/malq.200710011
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