The elementary theory of Abelian groups with m-chains of pure subgroups
We show that the field of rational numbers is not definable by a universal formula in Zilber's pseudo-exponential field.
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.