The Field of Reals with Multisummable Series and the Exponential Function

We show that the field of real numbers with multisummable real power series is model complete, o‐minimal and polynomially bounded. Further expansion by the exponential function yields again a model complete and o‐minimal structure which is exponentially bounded, and in which the Gamma function on the positive real line is definable. 2000 Mathematics Subject Classification: primary 03C10, 32B05, 32B20; secondary, 26E05.