H-fields and their Liouville extensions

Matthias Aschenbrenner, Lou Van Den Dries

Research output: Contribution to journalArticle

Abstract

We introduce H-fields as ordered differential fields of a certain kind. Hardy fields extending as well as the field of logarithmic-exponential series over are H-fields. We study Liouville extensions in the category of H-fields as a step towards a model theory of H-fields. The main result is that an H-field has at most two Liouville closures.

Original languageEnglish (US)
Pages (from-to)543-588
Number of pages46
JournalMathematische Zeitschrift
Volume242
Issue number3
DOIs
StatePublished - Dec 1 2002

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Model Theory
Logarithmic
Closure
Series

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

H-fields and their Liouville extensions. / Aschenbrenner, Matthias; Van Den Dries, Lou.

In: Mathematische Zeitschrift, Vol. 242, No. 3, 01.12.2002, p. 543-588.

Research output: Contribution to journalArticle

Aschenbrenner, Matthias ; Van Den Dries, Lou. / H-fields and their Liouville extensions. In: Mathematische Zeitschrift. 2002 ; Vol. 242, No. 3. pp. 543-588.
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