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

• Autores: Victor L. Selivanov
• Localización: Mathematical Logic Quarterly, ISSN 0942-5616, Vol. 53, Nº. 4-5, 2007, págs. 446-461
• Idioma: inglés
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• Resumen

  • 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.