Liouville closed H-fields

Matthias Aschenbrenner, Lou van den Dries

Research output: Contribution to journalArticle

Abstract

H-fields are fields with an ordering and a derivation subject to some compatibilities. (Hardy fields extending ℝ and fields of transseries over ℝ are H-fields.) We prove basic facts about the location of zeros of differential polynomials in Liouville closed H-fields, and study various constructions in the category of H-fields: closure under powers, constant field extension, completion, and building H-fields with prescribed constant field and H-couple. We indicate difficulties in obtaining a good model theory of H-fields, including an undecidability result. We finish with open questions that motivate our work.

Original languageEnglish (US)
Pages (from-to)83-139
Number of pages57
JournalJournal of Pure and Applied Algebra
Volume197
Issue number1-3
DOIs
StatePublished - May 1 2005

Fingerprint

Closed
Location of Zeros
Differential Polynomial
Undecidability
Field extension
Model Theory
Compatibility
Completion
Closure

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Liouville closed H-fields. / Aschenbrenner, Matthias; van den Dries, Lou.

In: Journal of Pure and Applied Algebra, Vol. 197, No. 1-3, 01.05.2005, p. 83-139.

Research output: Contribution to journalArticle

Aschenbrenner, Matthias ; van den Dries, Lou. / Liouville closed H-fields. In: Journal of Pure and Applied Algebra. 2005 ; Vol. 197, No. 1-3. pp. 83-139.
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