Publikation: kappa-bounded Exponential-Logarithmic Power Series Fields
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2005
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Shelah, Saharon
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Annals of Pure and Applied Logic. 2005, 136(3), pp. 284-296. ISSN 0168-0072. Available under: doi: 10.1016/j.apal.2005.04.001
Zusammenfassung
In [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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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Models of real exponentiation, Iterated lexicographic power of a chain, Logarithmic rank
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KUHLMANN, 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.2005.04.001BibTex
@article{Kuhlmann2005kappa-603,
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}
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