Comparison of Exponential-Logarithmic and Logarithmic-Exponential series


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KUHLMANN, 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

@article{Kuhlmann2012Compa-21244, title={Comparison of Exponential-Logarithmic and Logarithmic-Exponential series}, year={2012}, doi={10.1002/malq.201100113}, number={6}, volume={58}, issn={0942-5616}, journal={Mathematical Logic Quarterly}, pages={434--448}, author={Kuhlmann, Salma and Tressl, Marcus} }

<rdf:RDF xmlns:rdf="" xmlns:bibo="" xmlns:dc="" xmlns:dcterms="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dcterms:available rdf:datatype="">2013-01-25T10:44:58Z</dcterms:available> <dcterms:rights rdf:resource=""/> <dc:date rdf:datatype="">2013-01-25T10:44:58Z</dc:date> <dcterms:abstract xml:lang="eng">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.</dcterms:abstract> <bibo:uri rdf:resource=""/> <dcterms:issued>2012</dcterms:issued> <dc:rights>deposit-license</dc:rights> <dc:language>eng</dc:language> <dcterms:title>Comparison of Exponential-Logarithmic and Logarithmic-Exponential series</dcterms:title> <dc:contributor>Tressl, Marcus</dc:contributor> <dcterms:bibliographicCitation>Mathematical Logic Quarterly ; 58 (2012), 6. - S. 434-448</dcterms:bibliographicCitation> <dc:creator>Kuhlmann, Salma</dc:creator> <dc:creator>Tressl, Marcus</dc:creator> <dc:contributor>Kuhlmann, Salma</dc:contributor> </rdf:Description> </rdf:RDF>

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