Comparison of Exponential-Logarithmic and Logarithmic-Exponential series
Abstract
We explain how the field of logarithmic-exponential series constructed in DMM1 and DMM2 embeds as an exponential field in any field of exponential-logarithmic series constructed in KK1, K and 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(an, exp); the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.
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