Abstract
We deal with the Borel and difference hierarchies in the space Pω of all subsets of ω endowed with the Scott topology. (The spaces Pω and 2ω coincide set-theoretically but differ topologically.) We look at the Wadge reducibility in Pω. The results obtained are applied to the problem of characterizing ω 1-terms t which satisfy C = t(Σ10) for a given Borel-Wadge class C. We give its solution for some levels of the Wadge hierarchy, in particular, all levels of the Hausdorff difference hierarchy. Finally, we come up with a discussion of some relevant facts and open questions.
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