Model completeness for the differential field of transseries with exponentiation
Logic
2020-11-30 v3 Commutative Algebra
Abstract
Let be the differential field of logarithmic-exponential transseries. We show that the expansion of 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 by this exponential function and by its natural restricted sine and restricted cosine functions is also model complete and locally o-minimal.
Keywords
Cite
@article{arxiv.2004.14957,
title = {Model completeness for the differential field of transseries with exponentiation},
author = {Elliot Kaplan},
journal= {arXiv preprint arXiv:2004.14957},
year = {2020}
}
Comments
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