Comparison of exponential-logarithmic and logarithmic-exponential series

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Mathematical Logic Quarterly 58 (6):434-448 (2012)
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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 Thequation image; the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions

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10.1002/malq.201100113

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Citations of this work

Surreal ordered exponential fields.Philip Ehrlich & Elliot Kaplan - 2021 - Journal of Symbolic Logic 86 (3):1066-1115.

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References found in this work

Logarithmic-exponential series.Lou van den Dries, Angus Macintyre & David Marker - 2001 - Annals of Pure and Applied Logic 111 (1-2):61-113.
Schanuel's conjecture and free exponential rings.Angus Macintyre - 1991 - Annals of Pure and Applied Logic 51 (3):241-246.
Κ -bounded exponential-logarithmic power series fields.Salma Kuhlmann & Saharon Shelah - 2005 - Annals of Pure and Applied Logic 136 (3):284-296.

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