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  1. Comparison of exponential-logarithmic and logarithmic-exponential series.Salma Kuhlmann & Marcus Tressl - 2012 - Mathematical Logic Quarterly 58 (6):434-448.
    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 (...)
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  • Surreal ordered exponential fields.Philip Ehrlich & Elliot Kaplan - 2021 - Journal of Symbolic Logic 86 (3):1066-1115.
    In 2001, the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway’s ordered field ${\mathbf {No}}$ of surreal numbers was brought to the fore by the first author and employed to provide necessary and sufficient conditions for an ordered field to be isomorphic to an initial subfield of ${\mathbf {No}}$, i.e. a subfield of ${\mathbf {No}}$ that is an initial subtree of ${\mathbf {No}}$. In this sequel, analogous results are established for ordered exponential fields, making use of a slight generalization of (...)
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