A failure of quantifier elimination.
We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.
We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.
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.