Real Algebraic and Analytic Geometry
homepages: http://www.math.uic.edu/~maschenb/, http://www.math.uiuc.edu/People/vddries.html
Submission: 2004, February 16.
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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