Real Algebraic and Analytic Geometry

Preprint Server

Previous   Next
23. Matthias Aschenbrenner, Lou van den Dries:
Liouville Closed H-Fields.

e-mail: ,

Submission: 2002, November 7.

$H$-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.

Full text, 55p.: dvi 271k, ps.gz 170k, pdf 445k.

Server Home Page