Comparison of Exponential-Logarithmic and Logarithmic-Exponential series

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2012
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Tressl, Marcus
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urn:nbn:de:bsz:352-212442
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10.1002/malq.201100113
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Mathematical Logic Quarterly ; 58 (2012), 6. - pp. 434-448. - ISSN 0942-5616. - eISSN 1521-3870
Abstract
We explain how the field of logarithmic-exponential series constructed in L. van den Dries, A. Macintyre, and D. Marker: "Logarithmic-Exponential power series" and L. van den Dries, A. Macintyre, and D. Marker: "Logarithmic-Exponential series" embeds as an exponential field in any field of exponential-logarithmic series constructed in F.-V. Kuhlmann and S. Kuhlmann: "Explicit construction of exponential-logarithmic power series", S. Kuhlmann: "Ordered Exponential Fields" and S. Kuhlmann and S. Shelah: "κ–bounded Exponential Logarithmic Power Series Fields". 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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510 Mathematics
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generalized power series,Hahn groups,exponential extension,exponential closure,growth axioms,morphisms of prelogarithmic fields
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ISO 690KUHLMANN, Salma, Marcus TRESSL, 2012. Comparison of Exponential-Logarithmic and Logarithmic-Exponential series. In: Mathematical Logic Quarterly. 58(6), pp. 434-448. ISSN 0942-5616. eISSN 1521-3870. Available under: doi: 10.1002/malq.201100113
BibTex
@article{Kuhlmann2012Compa-21244,
  year={2012},
  doi={10.1002/malq.201100113},
  title={Comparison of Exponential-Logarithmic and Logarithmic-Exponential series},
  number={6},
  volume={58},
  issn={0942-5616},
  journal={Mathematical Logic Quarterly},
  pages={434--448},
  author={Kuhlmann, Salma and Tressl, Marcus}
}
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