Quantifier elimination for elementary geometry and elementary affine geometry

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...

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Detalles Bibliográficos
Publicado: 2012
Materias:
Affine geometry
Euclidean geometry
Geometric constructions
Quantifier elimination
Semi-algebraic geometry
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09425616_v58_n6_p399_Grimson
http://hdl.handle.net/20.500.12110/paper_09425616_v58_n6_p399_Grimson
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_09425616_v58_n6_p399_Grimson
record_format dspace
spelling paper:paper_09425616_v58_n6_p399_Grimson2023-06-08T15:53:35Z Quantifier elimination for elementary geometry and elementary affine geometry Affine geometry Euclidean geometry Geometric constructions Quantifier elimination Semi-algebraic geometry 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. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09425616_v58_n6_p399_Grimson http://hdl.handle.net/20.500.12110/paper_09425616_v58_n6_p399_Grimson
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Affine geometry
Euclidean geometry
Geometric constructions
Quantifier elimination
Semi-algebraic geometry
spellingShingle Affine geometry
Euclidean geometry
Geometric constructions
Quantifier elimination
Semi-algebraic geometry
Quantifier elimination for elementary geometry and elementary affine geometry
topic_facet Affine geometry
Euclidean geometry
Geometric constructions
Quantifier elimination
Semi-algebraic geometry
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. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
title Quantifier elimination for elementary geometry and elementary affine 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
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09425616_v58_n6_p399_Grimson
http://hdl.handle.net/20.500.12110/paper_09425616_v58_n6_p399_Grimson
_version_ 1768545745820975104

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