The Real Field with the Rational Points of an Elliptic Curve

@inproceedings{Hieronymi2009TheRF,
  title={The Real Field with the Rational Points of an Elliptic Curve},
  author={Philipp Hieronymi},
  year={2009}
}
We consider the expansion of the real field by a subgroup of a one-dimensional definable group satisfying a certain diophantine condition. The main example is the group of rational points of an elliptic curve over a number field. 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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