The real field with the rational points of an elliptic curve
Volume 211 / 2011
Fundamenta Mathematicae 211 (2011), 15-40
MSC: 03C10, 03C64, 14H52, 11U09.
DOI: 10.4064/fm211-1-2
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.
