Relative differential closure in Hardy fields

Autor:	Aschenbrenner, Matthias, Dries, Lou van den, van der Hoeven, Joris
Rok vydání:	2024
Předmět:	Mathematics - Logic Mathematics - Classical Analysis and ODEs Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	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. Comment: 24 pp. (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.)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.10764 Zobrazit plný text záznamu View this record from Arxiv