Model completeness for the differential field of transseries with exponentiation

Abstract

Let $\mathbb{T}$ be the differential field of logarithmic-exponential transseries. We show that the expansion of $\mathbb{T}$ by its natural exponential function is model complete and locally o-minimal. We give an axiomatization of the theory of this expansion that is effective relative to the theory of the real exponential field. We adapt our results to show that the expansion of $\mathbb{T}$ by this exponential function and by its natural restricted sine and restricted cosine functions is also model complete and locally o-minimal.

1.3 is incorrect as stated. This creates a gap in 4.15 and 4.19, both of which are needed for the main result. The gap in 4.15 can be fixed, the gap in 4.19 is work in progress