18 citations · 69 across the 34 of their papers we have counts for
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Short Hardy fields
Matthias Aschenbrenner, Lou van den Dries
Differentially algebraic Hardy field extensions of short Hardy fields are short. This is proved in the more general setting of -fields. As an application we extend a theorem of…
Relative differential closure in Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
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 conj…
The theory of maximal Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that all maximal Hardy fields are elementarily equivalent as differential fields to the differential field of transseries, and give various applications of this…
Analytic Hardy fields
Matthias Aschenbrenner, Lou van den Dries
We show that maximal analytic Hardy fields are in the sense of Hausdorff. We also prove various embedding theorems about analytic Hardy fields. For example, the ordered diffe…
Filling gaps in Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
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.
Maximal Hardy Fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
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…