On a differential intermediate value property

Authors

  • Matthias Aschenbrenner Kurt Gödel Research Center for Mathematical Logic, Universität Wien, 1090 Wien, Austria
  • Lou van den Dries Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.
  • Joris van der Hoeven CNRS, LIX, Ecole Polytechnique, 91128 Palaiseau Cedex, France

DOI:

https://doi.org/10.33044/revuma.2892

Abstract

Liouville closed $H$-fields are ordered differential fields where the ordering and derivation interact in a natural way and every linear differential equation of order $1$ has a nontrivial solution. (The introduction gives a precise definition.) For a Liouville closed $H$-field $K$ with small derivation we show that $K$ has the Intermediate Value Property for differential polynomials if and only if $K$ is elementarily equivalent to the ordered differential field of transseries. We also indicate how this applies to Hardy fields.

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Published

2022-03-18