### $\kappa$-bounded Exponential-Logarithmic Power Series Fields

by Kuhlmann and Shelah. [KuSh:857]

Annals Pure and Applied Logic, 2005

In [KKSh:601] 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 kappa
regular uncountable cardinal, 2^{kappa} pairwise non-isomorphic
models of real exponentiation (of cardinality kappa), but all
isomorphic as ordered fields. Indeed, the 2^{kappa} exponentials
constructed have pairwise distinct growth rates . This method
relies on constructing lexicographic chains with many automorphisms.

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