Real Algebraic and Analytic Geometry |

Liouville Closed H-Fields.

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homepages: http://www.math.uic.edu/~maschenb/,
http://www.math.uiuc.edu/People/vddries.html

Submission: 2002, November 7.

*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.*

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