2021/05/26 by Matthias Aschenbrenner, Lou van den Dries, Aschenbrenner, Matthias +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Logic (math.LO) #Meromorphic and Entire Functions
paper · doi:10.48550/arxiv.2105.12631
openalex publication_date 2021/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 K with small derivation we show: K has the Intermediate Value Property for differential polynomials iff K is elementarily equivalent to the ordered differential field of transseries. We also indicate how this applies to Hardy fields.