Logarithmic-exponential series

Lou van den Dries, Angus MacIntyre, David Marker

Research output: Contribution to journalArticle

Abstract

We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of "logarithmic-exponential series" (LE-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.

Original languageEnglish (US)
Pages (from-to)61-113
Number of pages53
JournalAnnals of Pure and Applied Logic
Volume111
Issue number1-2
DOIs
StatePublished - Jul 20 2001

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Logarithmic
Series
Differential Algebra
Laurent Series
Invert
Exponentiation
Subfield
Derivative
Operator

ASJC Scopus subject areas

  • Logic

Cite this

Logarithmic-exponential series. / van den Dries, Lou; MacIntyre, Angus; Marker, David.

In: Annals of Pure and Applied Logic, Vol. 111, No. 1-2, 20.07.2001, p. 61-113.

Research output: Contribution to journalArticle

van den Dries, Lou ; MacIntyre, Angus ; Marker, David. / Logarithmic-exponential series. In: Annals of Pure and Applied Logic. 2001 ; Vol. 111, No. 1-2. pp. 61-113.
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