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

Authors: Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven

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