kappa-bounded Exponential-Logarithmic Power Series Fields

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dc.creatorKuhlmann, Salma
dc.creatorShelah, Saharon
dc.date2005-12-10
dc.date.accessioned2026-07-07T06:55:02Z
dc.date.available2026-07-07T06:55:02Z
dc.descriptionIn 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.
dc.identifierhttps://arxiv.org/abs/math/0512220
dc.identifierhttp://arxiv.org/abs/math/0512220
dc.identifierAnnals of Pure and Applied Logic 136(2005):284-296
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106158
dc.subjectLogic
dc.subjectCommutative Algebra
dc.subjectRings and Algebras
dc.titlekappa-bounded Exponential-Logarithmic Power Series Fields
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