Liouville closed H-fields

Matthias Aschenbrenner, Lou van den Dries

Research output: Contribution to journalArticlepeer-review


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
Issue number1-3
StatePublished - May 1 2005

ASJC Scopus subject areas

  • Algebra and Number Theory


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