Work

Relative differential closure in Hardy fields

Year: 2025

Type: article

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 (J. Anal. Math. 39 , 235–255, 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.

Source: Monatshefte für Mathematik

DOI: 10.1007/s00605-025-02077-y

Authors: Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven

Institutions: University of Vienna, University of Illinois Urbana-Champaign, Centre National de la Recherche Scientifique, Laboratoire d'Informatique de l'École Polytechnique

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: European Commission, Universität Wien, HORIZON EUROPE European Research Council