Annals of Pure and Applied Logic 111 (1-2):61-113 (2001)

Abstract
We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of “logarithmic-exponential series” , which is equipped with a well behaved exponentiation. We show that the LE-series with derivative 0 are exactly the real constants, and we invert operators to show that each LE-series has a formal integral. We give evidence for the conjecture that the field of LE-series is a universal domain for ordered differential algebra in Hardy fields. We define composition of LE-series and establish its basic properties, including the existence of compositional inverses. Various interesting subfields of the field of LE-series are also considered
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DOI 10.1016/s0168-0072(01)00035-5
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Every Real Closed Field has an Integer Part.M. H. Mourgues & J. P. Ressayre - 1993 - Journal of Symbolic Logic 58 (2):641-647.

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Citations of this work BETA

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Κ -Bounded Exponential-Logarithmic Power Series Fields.Salma Kuhlmann & Saharon Shelah - 2005 - Annals of Pure and Applied Logic 136 (3):284-296.

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