Wadge hardness in Scott spaces and its effectivization

@article{Becher2014WadgeHI,
  title={Wadge hardness in Scott spaces and its effectivization},
  author={Ver{\'o}nica Becher and Serge Grigorieff},
  journal={Mathematical Structures in Computer Science},
  year={2014},
  volume={25},
  pages={1520 - 1545}
}
We prove some results on the Wadge order on the space of sets of natural numbers endowed with Scott topology, and more generally, on omega-continuous domains. Using alternating decreasing chains we characterize the property of Wadge hardness for the classes of the Hausdorff difference hierarchy (iterated differences of open sets). A similar characterization holds for Wadge one-to-one and finite-to-one completeness. We consider the same questions for the effectivization of the Wadge relation. We… 
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