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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todo:paper_09425616_v58_n6_p399_Grimson2023-10-03T15:49:01Z Quantifier elimination for elementary geometry and elementary affine geometry Grimson, R. Kuijpers, B. Othman, W. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Grimson, R. Kuijpers, B. Othman, W. 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. |
| format |
JOUR |
| author |
Grimson, R. Kuijpers, B. Othman, W. |
| author_facet |
Grimson, R. Kuijpers, B. Othman, W. |
| author_sort |
Grimson, R. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_09425616_v58_n6_p399_Grimson |
| work_keys_str_mv |
AT grimsonr quantifiereliminationforelementarygeometryandelementaryaffinegeometry AT kuijpersb quantifiereliminationforelementarygeometryandelementaryaffinegeometry AT othmanw quantifiereliminationforelementarygeometryandelementaryaffinegeometry |
| _version_ |
1807319178797907968 |