Comparison of Exponential-Logarithmic and Logarithmic-Exponential series
Logic
2013-01-01 v1 Commutative Algebra
Abstract
We explain how the field of logarithmic-exponential series constructed in \cite{DMM1} and \cite {DMM2} embeds as an exponential field in any field of exponential-logarithmic series constructed in \cite{KK1}, \cite {K} and \cite {KS}. On the other hand, we explain why no field of exponential-logarithmic series embeds in the field of logarithmic-exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non-isomorphic models of Th; the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.
Keywords
Cite
@article{arxiv.1112.4189,
title = {Comparison of Exponential-Logarithmic and Logarithmic-Exponential series},
author = {Marcus Tressl and Salma Kuhlmann},
journal= {arXiv preprint arXiv:1112.4189},
year = {2013}
}