Borel-amenable reducibilities for sets of reals

Journal of Symbolic Logic 74 (1):27-49 (2009)
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Abstract

We show that if Ƒ is any "well-behaved" subset of the Borei functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $P(^\omega \omega )$ induced by Ƒ turns out to look like the Wadge hierarchy (which is the special case where Ƒ is the set of continuous functions)

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10.2178/jsl/1231082301

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Citations of this work

Constructing wadge classes.Raphaël Carroy, Andrea Medini & Sandra Müller - 2022 - Bulletin of Symbolic Logic 28 (2):207-257.
Baire reductions and good Borel reducibilities.Luca Motto Ros - 2010 - Journal of Symbolic Logic 75 (1):323-345.
Continuous reducibility and dimension of metric spaces.Philipp Schlicht - 2018 - Archive for Mathematical Logic 57 (3-4):329-359.
Beyond Borel-amenability: scales and superamenable reducibilities.Luca Motto Ros - 2010 - Annals of Pure and Applied Logic 161 (7):829-836.

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References found in this work

More on Wadge determinacy.Alessandro Andretta - 2006 - Annals of Pure and Applied Logic 144 (1-3):2-32.
Equivalence between Wadge and Lipschitz determinacy.Alessandro Andretta - 2003 - Annals of Pure and Applied Logic 123 (1-3):163-192.
Beyond Borel-amenability: scales and superamenable reducibilities.Luca Motto Ros - 2010 - Annals of Pure and Applied Logic 161 (7):829-836.
Decomposing baire functions.J. Cichoń, M. Morayne, J. Pawlikowski & S. Solecki - 1991 - Journal of Symbolic Logic 56 (4):1273 - 1283.

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