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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/256473
Ver los metadatos del registro completo
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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 Técnicas2025-09-03T10:11:36Zoai: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:34982025-09-03 10:11:36.639CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.13397 |