05834949

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05834949 G\"unayd\i n, Ayhan Hieronymi, Philipp The real field with the rational points of an elliptic curve. Fundam. Math. 211, No. 1, 15-40 (2011). 2011 Instytut Matematyczny PAN, Warszawa EN real field rational points elliptic curve definable set open core

doi:10.4064/fm211-1-2

Summary: 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.