Comparison of exponential-logarithmic and logarithmic-exponential series

Salma Kuhlmann, Marcus Tressl

    Research output: Contribution to journalArticlepeer-review

    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 Th(R{double-struck} an, exp the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.
    Original languageEnglish
    Pages (from-to)434-448
    Number of pages15
    JournalMathematical Logic Quarterly
    Volume58
    Issue number6
    DOIs
    Publication statusPublished - Nov 2012

    Keywords

    • Exponential closure
    • Exponential extension
    • Generalized power series
    • Growth axioms
    • Hahn groups
    • Morphisms of prelogarithmic fields

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