Geodesic
Effective Wadge hierarchy in computable quasi-Polish spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 121-135

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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.
Keywords: computable quasi-Polish space, effective Wadge hierarchy, fine hierarchy, preservation property, effective Hausdorff theorem.
Mots-clés : $k$-partition 
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     author = {V. L. Selivanov},
     title = {Effective {Wadge} hierarchy in computable {quasi-Polish} spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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V. L. Selivanov. Effective Wadge hierarchy in computable quasi-Polish spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 121-135. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a2/