| Résume | Assuming Schanuel's conjecture from transcendental number theory, we prove that the complete first-order theory of the real exponential field is axiomatized by the axioms of definably complete exponential fields satisfying the differential equation exp'=exp. We deduce our main theorem from an unconditional model completeness result for definably complete expansions of fields by an exponential function restricted to the open interval (-1,1). The talk is based on joint work with Alessandro Berarducci and Marcello Mamino. |
