Comparison of Exponential-Logarithmic and Logarithmic-Exponential series

Kuhlmann, Salma; Tressl, Marcus

Comparison of Exponential-Logarithmic and Logarithmic-Exponential series

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Datum

2012

Autor:innen

Kuhlmann, Salma

Tressl, Marcus

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Mathematical Logic Quarterly. 2012, 58(6), pp. 434-448. ISSN 0942-5616. eISSN 1521-3870. Available under: doi: 10.1002/malq.201100113

Zusammenfassung

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

generalized power series, Hahn groups, exponential extension, exponential closure, growth axioms, morphisms of prelogarithmic fields

Zitieren

ISO 690

KUHLMANN, Salma, Marcus TRESSL, 2012. Comparison of Exponential-Logarithmic and Logarithmic-Exponential series. In: Mathematical Logic Quarterly. 2012, 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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