Relative differential closure in Hardy fields

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.

25 pp., revised after comments by referees. (Submitted to special edition of Monatshefte für Mathematik commemorating the centenary of K. Gödel's enrollment as a student at the University of Vienna.). arXiv admin note: text overlap with arXiv:2304.10846