Comparison of Exponential-Logarithmic and Logarithmic-Exponential series

Details Comparison of Exponential-Logarithmic and Logarithmic-Exponential series Comparison of Exponential-Logarithmic and Logarithmic-Exponential series

2011-12-18

arxiv.org/abs/1112.4189v1

Mathematics

Logic

Scientific paper

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$(\R_{an, exp})$; the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.

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