Real Algebraic and Analytic Geometry |

Asymptotic Differential Algebra.

e-mail: ,

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

Submission: 2004, February 16.

*Abstract:
We believe there is room for a subject named as in the
title of this paper. Motivating examples are Hardy fields and fields of
transseries. Assuming no previous knowledge of these notions, we
introduce both, state some of their basic properties, and explain
connections to o-minimal structures. We describe a common algebraic
framework for these examples: the category of $H$-fields. This
unified setting leads to a better understanding of Hardy fields
and transseries from an algebraic and model-theoretic perspective.*

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