Filling gaps in Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
TL;DR
This paper introduces a method to fill countable gaps in Hardy fields, demonstrating that any two maximal Hardy fields are back-and-forth equivalent, thus advancing the understanding of their structural properties.
Contribution
It provides a novel technique for filling gaps in Hardy fields and establishes the back-and-forth equivalence of maximal Hardy fields.
Findings
Successfully fills countable gaps in Hardy fields.
Proves maximal Hardy fields are back-and-forth equivalent.
Enhances structural understanding of Hardy fields.
Abstract
We show how to fill "countable" gaps in Hardy fields. We use this to prove that any two maximal Hardy fields are back-and-forth equivalent.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Housing, Finance, and Neoliberalism