Quantifier elimination for elementary geometry and elementary affine geometry

Autores
Grimson, Rafael; Kuijpers, Bart; Othman, Walied
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry (n ≥ 2), based on extending FO(β≡) and FO(β), respectively, with new function symbols. Here, β stands for the betweenness relation and ≡ for the congruence relation. We show that the associated theories admit effective quantifier elimination.
Fil: Grimson, Rafael. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Kuijpers, Bart. Universiteit Limburg; Bélgica
Fil: Othman, Walied. Universitat Zurich; Suiza
Materia
Affine Geometry
Euclidean Geometry
Geometric Constructions
Quantifier Elimination
Semi-Algebraic Geometry
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:11336/68254
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/68254
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Quantifier elimination for elementary geometry and elementary affine geometryGrimson, RafaelKuijpers, BartOthman, WaliedAffine GeometryEuclidean GeometryGeometric ConstructionsQuantifier EliminationSemi-Algebraic Geometryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry (n ≥ 2), based on extending FO(β≡) and FO(β), respectively, with new function symbols. Here, β stands for the betweenness relation and ≡ for the congruence relation. We show that the associated theories admit effective quantifier elimination.Fil: Grimson, Rafael. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kuijpers, Bart. Universiteit Limburg; BélgicaFil: Othman, Walied. Universitat Zurich; SuizaWiley VCH Verlag2012-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/68254Grimson, Rafael; Kuijpers, Bart; Othman, Walied; Quantifier elimination for elementary geometry and elementary affine geometry; Wiley VCH Verlag; Mathematical Logic Quarterly; 58; 6; 11-2012; 399-4160942-5616CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1002/malq.201100095info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/malq.201100095info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:00:08Zoai:ri.conicet.gov.ar:11336/68254instacron: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 10:00:08.698CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quantifier elimination for elementary geometry and elementary affine geometry
title Quantifier elimination for elementary geometry and elementary affine geometry
spellingShingle Quantifier elimination for elementary geometry and elementary affine geometry
Grimson, Rafael
Affine Geometry
Euclidean Geometry
Geometric Constructions
Quantifier Elimination
Semi-Algebraic Geometry
title_short Quantifier elimination for elementary geometry and elementary affine geometry
title_full Quantifier elimination for elementary geometry and elementary affine geometry
title_fullStr Quantifier elimination for elementary geometry and elementary affine geometry
title_full_unstemmed Quantifier elimination for elementary geometry and elementary affine geometry
title_sort Quantifier elimination for elementary geometry and elementary affine geometry
dc.creator.none.fl_str_mv Grimson, Rafael
Kuijpers, Bart
Othman, Walied
author Grimson, Rafael
author_facet Grimson, Rafael
Kuijpers, Bart
Othman, Walied
author_role author
author2 Kuijpers, Bart
Othman, Walied
author2_role author
author
dc.subject.none.fl_str_mv Affine Geometry
Euclidean Geometry
Geometric Constructions
Quantifier Elimination
Semi-Algebraic Geometry
topic Affine Geometry
Euclidean Geometry
Geometric Constructions
Quantifier Elimination
Semi-Algebraic Geometry
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry (n ≥ 2), based on extending FO(β≡) and FO(β), respectively, with new function symbols. Here, β stands for the betweenness relation and ≡ for the congruence relation. We show that the associated theories admit effective quantifier elimination.
Fil: Grimson, Rafael. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Kuijpers, Bart. Universiteit Limburg; Bélgica
Fil: Othman, Walied. Universitat Zurich; Suiza
description We introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry (n ≥ 2), based on extending FO(β≡) and FO(β), respectively, with new function symbols. Here, β stands for the betweenness relation and ≡ for the congruence relation. We show that the associated theories admit effective quantifier elimination.
publishDate 2012
dc.date.none.fl_str_mv 2012-11
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/11336/68254
Grimson, Rafael; Kuijpers, Bart; Othman, Walied; Quantifier elimination for elementary geometry and elementary affine geometry; Wiley VCH Verlag; Mathematical Logic Quarterly; 58; 6; 11-2012; 399-416
0942-5616
CONICET Digital
CONICET
url http://hdl.handle.net/11336/68254
identifier_str_mv Grimson, Rafael; Kuijpers, Bart; Othman, Walied; Quantifier elimination for elementary geometry and elementary affine geometry; Wiley VCH Verlag; Mathematical Logic Quarterly; 58; 6; 11-2012; 399-416
0942-5616
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1002/malq.201100095
info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/malq.201100095
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 Wiley VCH Verlag
publisher.none.fl_str_mv Wiley VCH Verlag
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
_version_ 1842269621663563776
score 13.13397

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