On a differential intermediate value property
نویسندگان
چکیده
Liouville closed $H$-fields are ordered differential fields whose ordering and derivation interact in a natural way where every linear equation of order $1$ has nontrivial solution. (The introduction gives precise definition.) For $H$-field $K$ with small we show: the Intermediate Value Property for polynomials iff is elementarily equivalent to field transseries. We also indicate how this applies Hardy fields.
منابع مشابه
A differential intermediate value theorem
In this survey paper, we outline the proof of a recent differential intermediate value theorem for transseries. Transseries are a generalization of power series with real coefficients, in which one allows the recursive appearance of exponentials and logarithms. Denoting by T the field of transseries, the intermediate value theorem states that for any differential polynomials P with coefficients...
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ژورنال
عنوان ژورنال: Revista De La Union Matematica Argentina
سال: 2022
ISSN: ['0041-6932', '1669-9637']
DOI: https://doi.org/10.33044/revuma.2892