2019/10/29 by Selivanov, Victor
#03D55 #03D78 #F.1.1 #F.2.1 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.1910.13220
We define and study an effective version of the Wadge hierarchy in computable quasi-Polish spaces which include most spaces of interest for computable analysis. Along with hierarchies of sets we study hierarchies of k-partitions which are interesting on their own. We show that levels of such hierarchies are preserved by the computable effectively open surjections, that if the effective Hausdorff-Kuratowski theorem holds in the Baire space then it holds in every computable quasi-Polish space, and we extend the effective Hausdorff theorem to k-partitions.