A Note on Exponential-logarithmic and Logarithmic-exponential Series
نویسندگان
چکیده
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(Ran, exp); the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.
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تاریخ انتشار 2008