Wadge hardness in Scott spaces and its effectivization

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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 (ite...

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Autor principal: Becher, Verónica Andrea
Publicado: 2014
Materias:
Hardness
Topology
Continuous domain
Difference hierarchies
Hausdorff
Natural number
One chain
Scott topology
Chains
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09601295_v39_n11_p_Becher
http://hdl.handle.net/20.500.12110/paper_09601295_v39_n11_p_Becher
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_09601295_v39_n11_p_Becher
record_format dspace
spelling paper:paper_09601295_v39_n11_p_Becher2023-06-08T15:57:34Z Wadge hardness in Scott spaces and its effectivization Becher, Verónica Andrea Hardness Topology Continuous domain Difference hierarchies Hausdorff Natural number One chain Scott topology Chains 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 also show that for the space of sets of natural numbers endowed with the Scott topology, in each class of the Hausdorff difference hierarchy there are two strictly increasing chains of Wadge degrees of sets properly in that class. The length of these chains is the rank of the considered class, and each element in one chain is incomparable with all the elements in the other chain. Copyright © Cambridge University Press 2014. Fil:Becher, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09601295_v39_n11_p_Becher http://hdl.handle.net/20.500.12110/paper_09601295_v39_n11_p_Becher
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Hardness
Topology
Continuous domain
Difference hierarchies
Hausdorff
Natural number
One chain
Scott topology
Chains
spellingShingle Hardness
Topology
Continuous domain
Difference hierarchies
Hausdorff
Natural number
One chain
Scott topology
Chains
Becher, Verónica Andrea
Wadge hardness in Scott spaces and its effectivization
topic_facet Hardness
Topology
Continuous domain
Difference hierarchies
Hausdorff
Natural number
One chain
Scott topology
Chains
description 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 also show that for the space of sets of natural numbers endowed with the Scott topology, in each class of the Hausdorff difference hierarchy there are two strictly increasing chains of Wadge degrees of sets properly in that class. The length of these chains is the rank of the considered class, and each element in one chain is incomparable with all the elements in the other chain. Copyright © Cambridge University Press 2014.
author Becher, Verónica Andrea
author_facet Becher, Verónica Andrea
author_sort Becher, Verónica Andrea
title Wadge hardness in Scott spaces and its effectivization
title_short Wadge hardness in Scott spaces and its effectivization
title_full Wadge hardness in Scott spaces and its effectivization
title_fullStr Wadge hardness in Scott spaces and its effectivization
title_full_unstemmed Wadge hardness in Scott spaces and its effectivization
title_sort wadge hardness in scott spaces and its effectivization
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09601295_v39_n11_p_Becher
http://hdl.handle.net/20.500.12110/paper_09601295_v39_n11_p_Becher
work_keys_str_mv AT becherveronicaandrea wadgehardnessinscottspacesanditseffectivization
_version_ 1768544144656957440

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