Mathematical Logic Quarterly 58 (6):434-448 (2012)

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
Keywords 13A18  12F20  MSC (2010) Primary: 06A05  generalized power series  Secondary: 03C60  12J15  growth axioms  Hahn groups  12L12  exponential closure  12J10  12F05  morphisms of prelogarithmic fields  exponential extension  12F10
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DOI 10.1002/malq.201100113
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References found in this work BETA

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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