Real Algebraic and Analytic Geometry

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117. Salma Kuhlmann, Saharon Shelah:
κ-bounded Exponential-Logarithmic Power Series Fields.

e-mail: ,

Submission: 2005, April 17.

In [K-K-S] 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 to construct for every κ regular uncountable cardinal, 2 κ pairwise non-isomorphic models of real exponentiation (of cardinality κ), but all isomorphic as ordered fields. Indeed, the 2 κ exponentials constructed have pairwise distinct growth rates. This method relies on constructing lexicographic chains with many automorphisms.

Mathematics Subject Classification (2000): 06A05, 03C60.

Full text, 14p.: dvi 59k, ps.gz 163k, pdf 204k.

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