The descriptive complexity of the set of Poisson generic numbers

Autores
Becher, Veronica Andrea; Jackson, Stephen; Kwietniak, Dominik; Mance, Bill
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let b ≥ 2 be an integer. We show that the set of real numbers that are Poisson generic in base b is Π0 3-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base b and not Poisson generic in base b is complete for the class given by the differences between Π0 3 sets. We also show that the effective versions of these results hold in the effective Borel hierarchy.
Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Fil: Jackson, Stephen. University of North Texas; Estados Unidos
Fil: Kwietniak, Dominik. Jagiellonian University In Krakow; Polonia
Fil: Mance, Bill. Adam Mickiewicz University In Poznań; Polonia
Materia
POISSON GENERIC SEQUENCES
DESCRIPTIVE COMPLEXITY
NORMAL NUMBERS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/256473
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/256473
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling The descriptive complexity of the set of Poisson generic numbersBecher, Veronica AndreaJackson, StephenKwietniak, DominikMance, BillPOISSON GENERIC SEQUENCESDESCRIPTIVE COMPLEXITYNORMAL NUMBERShttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1Let b ≥ 2 be an integer. We show that the set of real numbers that are Poisson generic in base b is Π0 3-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base b and not Poisson generic in base b is complete for the class given by the differences between Π0 3 sets. We also show that the effective versions of these results hold in the effective Borel hierarchy.Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Jackson, Stephen. University of North Texas; Estados UnidosFil: Kwietniak, Dominik. Jagiellonian University In Krakow; PoloniaFil: Mance, Bill. Adam Mickiewicz University In Poznań; PoloniaWorld Scientific2024-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/256473Becher, Veronica Andrea; Jackson, Stephen; Kwietniak, Dominik; Mance, Bill; The descriptive complexity of the set of Poisson generic numbers; World Scientific; Journal Of Mathematical Logic; 24500019; 5-2024; 1-180219-0613CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/10.1142/S0219061324500193info:eu-repo/semantics/altIdentifier/doi/10.1142/S0219061324500193info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:52:55Zoai:ri.conicet.gov.ar:11336/256473instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 10:52:55.634CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The descriptive complexity of the set of Poisson generic numbers
title The descriptive complexity of the set of Poisson generic numbers
spellingShingle The descriptive complexity of the set of Poisson generic numbers
Becher, Veronica Andrea
POISSON GENERIC SEQUENCES
DESCRIPTIVE COMPLEXITY
NORMAL NUMBERS
title_short The descriptive complexity of the set of Poisson generic numbers
title_full The descriptive complexity of the set of Poisson generic numbers
title_fullStr The descriptive complexity of the set of Poisson generic numbers
title_full_unstemmed The descriptive complexity of the set of Poisson generic numbers
title_sort The descriptive complexity of the set of Poisson generic numbers
dc.creator.none.fl_str_mv Becher, Veronica Andrea
Jackson, Stephen
Kwietniak, Dominik
Mance, Bill
author Becher, Veronica Andrea
author_facet Becher, Veronica Andrea
Jackson, Stephen
Kwietniak, Dominik
Mance, Bill
author_role author
author2 Jackson, Stephen
Kwietniak, Dominik
Mance, Bill
author2_role author
author
author
dc.subject.none.fl_str_mv POISSON GENERIC SEQUENCES
DESCRIPTIVE COMPLEXITY
NORMAL NUMBERS
topic POISSON GENERIC SEQUENCES
DESCRIPTIVE COMPLEXITY
NORMAL NUMBERS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let b ≥ 2 be an integer. We show that the set of real numbers that are Poisson generic in base b is Π0 3-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base b and not Poisson generic in base b is complete for the class given by the differences between Π0 3 sets. We also show that the effective versions of these results hold in the effective Borel hierarchy.
Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina
Fil: Jackson, Stephen. University of North Texas; Estados Unidos
Fil: Kwietniak, Dominik. Jagiellonian University In Krakow; Polonia
Fil: Mance, Bill. Adam Mickiewicz University In Poznań; Polonia
description Let b ≥ 2 be an integer. We show that the set of real numbers that are Poisson generic in base b is Π0 3-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base b and not Poisson generic in base b is complete for the class given by the differences between Π0 3 sets. We also show that the effective versions of these results hold in the effective Borel hierarchy.
publishDate 2024
dc.date.none.fl_str_mv 2024-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/256473
Becher, Veronica Andrea; Jackson, Stephen; Kwietniak, Dominik; Mance, Bill; The descriptive complexity of the set of Poisson generic numbers; World Scientific; Journal Of Mathematical Logic; 24500019; 5-2024; 1-18
0219-0613
CONICET Digital
CONICET
url http://hdl.handle.net/11336/256473
identifier_str_mv Becher, Veronica Andrea; Jackson, Stephen; Kwietniak, Dominik; Mance, Bill; The descriptive complexity of the set of Poisson generic numbers; World Scientific; Journal Of Mathematical Logic; 24500019; 5-2024; 1-18
0219-0613
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/10.1142/S0219061324500193
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0219061324500193
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.087074

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