On a Differential Intermediate Value Property
Logic
2021-05-27 v1
Abstract
Liouville closed -fields are ordered differential fields whose ordering and derivation interact in a natural way and where every linear differential equation of order has a nontrivial solution. (The introduction gives a precise definition.) For a Liouville closed -field with small derivation we show: has the Intermediate Value Property for differential polynomials iff is elementarily equivalent to the ordered differential field of transseries. We also indicate how this applies to Hardy fields.
Keywords
Cite
@article{arxiv.2105.12631,
title = {On a Differential Intermediate Value Property},
author = {Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven},
journal= {arXiv preprint arXiv:2105.12631},
year = {2021}
}
Comments
9 pp. arXiv admin note: text overlap with arXiv:1904.01069