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Quantifier elimination for elementary geometry and elementary affine geometry


Grimson, Rafael; Kuijpers, Bart; Othman, Walied (2012). Quantifier elimination for elementary geometry and elementary affine geometry. Mathematical Logic Quarterly, 58(6):399-416.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Geography
Dewey Decimal Classification:910 Geography & travel
Language:English
Date:2012
Deposited On:21 Feb 2013 08:54
Last Modified:05 Apr 2016 16:34
Publisher:Wiley-Blackwell
ISSN:0044-3050
Publisher DOI:https://doi.org/10.1002/malq.201100095

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