Relative differential closure in Hardy fields
Logic
2026-04-27 v2 Classical Analysis and ODEs
Dynamical Systems
Abstract
We study relative differential closure in the context of Hardy fields. Using our earlier work on algebraic differential equations over Hardy fields, this leads to a proof of a conjecture of Boshernitzan (1981): the intersection of all maximal analytic Hardy fields agrees with that of all maximal Hardy fields. We also generalize a key ingredient in the proof, and describe a cautionary example delineating the boundaries of its applicability.
Keywords
Cite
@article{arxiv.2412.10764,
title = {Relative differential closure in Hardy fields},
author = {Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven},
journal= {arXiv preprint arXiv:2412.10764},
year = {2026}
}
Comments
25 pp., revised after comments by referees. (Submitted to special edition of Monatshefte f\"ur Mathematik commemorating the centenary of K. G\"odel's enrollment as a student at the University of Vienna.). arXiv admin note: text overlap with arXiv:2304.10846