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.
A remark on Ax's theorem on solvability modulo primes.
Definable sets over finite fields.
Équations diophantiennes modulo
Geometrical model theory.
H. L. M. (Hrushovski-Lang-Mordell)
On the ranges of discrete exponentials.
The real field with the rational points of an elliptic curve
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.
Uniform p-adic cell decomposition and local zeta functions.