Hierarchies of Δ 0 2 ‐measurable k‐partitions

Mathematical Logic Quarterly 53 (4-5):446-461 (2007)
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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 Δ02‐measurable k ‐partitions of the Baire space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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10.1002/malq.200710011

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The Hausdorff-Ershov Hierarchy in Euclidean Spaces.Armin Hemmerling - 2006 - Archive for Mathematical Logic 45 (3):323-350.

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