Quantifier elimination for elementary geometry and elementary affine geometry

Authors

  • Rafael Grimson,

    Corresponding author
    1. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
    • Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
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  • Bart Kuijpers,

    1. Theoretical Computer Science Group, Hasselt University & Transnationale Universiteit Limburg, Agoralaan, Gebouw D, 3590 Diepenbeek, Belgium
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  • Walied Othman

    1. Geographisches Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
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Abstract

We introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry (n ≥ 2), based on extending equation image and equation image, 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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