The real field with the rational points of an elliptic curve

Details The real field with the rational points of an elliptic curve The real field with the rational points of an elliptic curve

2009-06-02

arxiv.org/abs/0906.0528v5

Fundamenta Mathematicae 211 (2011) 15-40

Mathematics

Logic

Scientific paper

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.

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