Submission date: 2 June 2009.

Abstract:

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.

Mathematics Subject Classification: 03C10, 03C64, 14H52, 11U09

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