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On a differential intermediate value property
Volume 64, no. 1
(2022),
pp. 1–10
https://doi.org/10.33044/revuma.2892
Abstract
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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Published by the Unión Matemática Argentina |
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