Quantifier elimination for elementary geometry and elementary affine geometry

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Mathematical Logic Quarterly 58 (6):399-416 (2012)
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Abstract

We introduce new first-order languages for the elementary n-dimensional geometry and elementary n-dimensional affine geometry , 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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10.1002/malq.201100095

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Mathematical logic.Joseph Robert Shoenfield - 1967 - Reading, Mass.,: Addison-Wesley.
A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1952 - Journal of Symbolic Logic 17 (3):207-207.
Tarski's system of geometry.Alfred Tarski & Steven Givant - 1999 - Bulletin of Symbolic Logic 5 (2):175-214.
La Géométrie.René Descartes & Franz Hals - 1927 - Revue de Métaphysique et de Morale 34 (4):3-4.

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