Real Algebraic and Analytic Geometry |

κ-bounded Exponential-Logarithmic Power Series Fields.

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Submission: 2005, April 17.

*Abstract:
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.

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