Baire reductions and good Borel reducibilities

Abstract

In reference [8] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [8] allowing to deal with a larger class of notions of reduction (including, among others, the Baire class $\xi$ functions).

21 pages

Cited by in corpus (6)

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• Beyond Borel-amenability: scales and superamenable reducibilities
• Bad Wadge-like reducibilities on the Baire space
• Game representations of classes of piecewise definable functions