Comparison of exponential‐logarithmic and logarithmic‐exponential series

Abstract We explain how the field of logarithmic‐exponential series constructed in 20 and 21 embeds as an exponential field in any field of exponential‐logarithmic series constructed in 9 , 6 , and 13 . 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\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$(\mathbb {R}_{\mbox{an, exp}})$\end{document} ; the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.