On a differential intermediate value property

• Matthias Aschenbrenner ^[2] ; Lou van Den Dries ^[3] ; Joris van Der Hoeven ^[1]
  1. [1] Centre National de la Recherche Scientifique

     Centre National de la Recherche Scientifique

     París, Francia

     
  2. [2] Universit¨at Wien, Austria
  3. [3] University of Illinois at Urbana-Champaign, USA

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• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 64, Nº. Extra 1, 2022, págs. 1-10
• Idioma: inglés
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• Resumen

  • 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.