On the real exponential field with restricted analytic functions

The model-theoretic structure (ℝ_an, exp) is investigated as a special case of an expansion of the field of reals by certain families of C ^∞-functions. In particular, we use methods of Wilkie to show that (ℝ_an, exp) is (finitely) model complete and O-minimal. We also prove analytic cell decomposition and the fact that every definable unary function is ultimately bounded by an iterated exponential function.