English

Maximal Hardy Fields

Logic 2025-02-18 v3 Classical Analysis and ODEs Dynamical Systems

Abstract

We show that all maximal Hardy fields are elementarily equivalent as differential fields, and give various applications of this result and its proof. We also answer some questions on Hardy fields posed by Boshernitzan.

Keywords

Cite

@article{arxiv.2304.10846,
  title  = {Maximal Hardy Fields},
  author = {Matthias Aschenbrenner and Lou van den Dries and Joris van der Hoeven},
  journal= {arXiv preprint arXiv:2304.10846},
  year   = {2025}
}

Comments

472 pp. This document is not intended for publication in its current form. V3: reformulated a wrong identity just before 7.6.24, and accordingly corrected some proofs following it

R2 v1 2026-06-28T10:13:30.414Z