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Preprint Number 403

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403. Marcus Tressl and Salma Kuhlmann
Comparison of Exponential-Logarithmic and Logarithmic-Exponential series
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Submission date: 18 December 2011.

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(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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Full text arXiv 1112.4189: pdf, ps.


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