Borel-amenable Reducibilities for Sets of Reals

Details Borel-amenable Reducibilities for Sets of Reals Borel-amenable Reducibilities for Sets of Reals

2008-04-30

arxiv.org/abs/0804.4800v1

Journal of Symbolic Logic 74 (2009), no. 1, 27-49

Mathematics

Logic

21 pages

Scientific paper

We show that if $\mathcal{F}$ is any "well-behaved" subset of the Borel
functions and we assume the Axiom of Determinacy then the hierarchy of degrees
on $\pow(\mathbb{R})$ induced by $\mathcal{F}$ turns out to look like the Wadge
hierarchy (which is the special case where $\mathcal{F}$ is the set of
continuous functions).

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