kappa-bounded Exponential-Logarithmic Power Series Fields

Kurzanzeige
dc.contributor.authorKuhlmann, Salma
dc.contributor.authorShelah, Saharondeu
dc.date.accessioned2011-03-22T17:45:12Zdeu
dc.date.available2011-03-22T17:45:12Zdeu
dc.date.issued2005
dc.description.abstractIn [F.-V. Kuhlmann, S. Kuhlmann, S. Shelah, Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 (1997) 3177 3183] it was shown that fields of generalized power series cannot admit an exponential function. In this paper, we construct fields of generalized power series with bounded support which admit an exponential. We give a natural definition of an exponential, which makes these fields into models of real exponentiation. The method allows us to construct for every κ regular uncountable cardinal, 2κ pairwise non-isomorphic models of real exponentiation (of cardinality κ), but all isomorphic as ordered fields. Indeed, the 2κ exponentials constructed have pairwise distinct growth rates. This method relies on constructing lexicographic chains with many automorphisms.eng
dc.description.versionpublished
dc.format.mimetypeapplication/pdfdeu
dc.identifier.citationFirst publ. in: Annals of pure and applied logic 136 (2005), 3, pp. 284-296deu
dc.identifier.doi10.1016/j.apal.2005.04.001eng
dc.identifier.ppn313492824deu
dc.identifier.urihttp://kops.uni-konstanz.de/handle/123456789/603
dc.language.isoengdeu
dc.legacy.dateIssued2009deu
dc.rightsterms-of-usedeu
dc.rights.urihttps://rightsstatements.org/page/InC/1.0/deu
dc.subjectModels of real exponentiationdeu
dc.subjectIterated lexicographic power of a chaindeu
dc.subjectLogarithmic rankdeu
dc.subject.ddc510deu
dc.subject.msc06A05deu
dc.subject.msc03C60deu
dc.titlekappa-bounded Exponential-Logarithmic Power Series Fieldseng
dc.typeJOURNAL_ARTICLEdeu
dspace.entity.typePublication
kops.citation.bibtex
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  year={2005},
  doi={10.1016/j.apal.2005.04.001},
  title={kappa-bounded Exponential-Logarithmic Power Series Fields},
  number={3},
  volume={136},
  issn={0168-0072},
  journal={Annals of Pure and Applied Logic},
  pages={284--296},
  author={Kuhlmann, Salma and Shelah, Saharon}
}
kops.citation.iso690KUHLMANN, Salma, Saharon SHELAH, 2005. kappa-bounded Exponential-Logarithmic Power Series Fields. In: Annals of Pure and Applied Logic. 2005, 136(3), pp. 284-296. ISSN 0168-0072. Available under: doi: 10.1016/j.apal.2005.04.001deu
kops.citation.iso690KUHLMANN, Salma, Saharon SHELAH, 2005. kappa-bounded Exponential-Logarithmic Power Series Fields. In: Annals of Pure and Applied Logic. 2005, 136(3), pp. 284-296. ISSN 0168-0072. Available under: doi: 10.1016/j.apal.2005.04.001eng
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