Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9497137 | Journal of Pure and Applied Algebra | 2005 | 57 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Matthias Aschenbrenner, Lou van den Dries,