Κ -bounded exponential-logarithmic power series fields

Annals of Pure and Applied Logic 136 (3):284-296 (2005)
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Abstract

In [F.-V. Kuhlmann, S. Kuhlmann, S. Shelah, Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 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 , 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

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Citations of this work

Surreal ordered exponential fields.Philip Ehrlich & Elliot Kaplan - 2021 - Journal of Symbolic Logic 86 (3):1066-1115.

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References found in this work

Logarithmic-exponential series.Lou van den Dries, Angus Macintyre & David Marker - 2001 - Annals of Pure and Applied Logic 111 (1-2):61-113.
Lexicographic Exponentiation of Chains.W. C. Holland, S. Kuhlmann & S. H. McCleary - 2005 - Journal of Symbolic Logic 70 (2):389 - 409.

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