kappa-bounded Exponential-Logarithmic Power Series Fields

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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.

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Logic, Commutative Algebra, Rings and Algebras

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http://salesiana.dossiersoluciones.com/handle/123456789/106158

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0512220
 http://arxiv.org/abs/math/0512220
 Annals of Pure and Applied Logic 136(2005):284-296

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arXiv