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Resumen de On a differential intermediate value property

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

  • 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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