kappa-bounded Exponential-Logarithmic Power Series Fields
Logic
2007-05-23 v1 Commutative Algebra
Rings and Algebras
Abstract
In math.AC/9608214 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.
Cite
@article{arxiv.math/0512220,
title = {kappa-bounded Exponential-Logarithmic Power Series Fields},
author = {Salma Kuhlmann and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0512220},
year = {2007}
}