The real field with the rational points of an elliptic curve

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Abstract

We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets definable in that structure are semialgebraic. © Instytut Matematyczny PAN, 2011.

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Günaydin, A., & Hieronymi, P. (2011). The real field with the rational points of an elliptic curve. Fundamenta Mathematicae, 211(1), 15–40. https://doi.org/10.4064/fm211-1-2

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