8 citations · 24 across the 14 of their papers we have counts for
4 papers · 1 filter
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…
Constructing -free Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that every Hardy field extends to an -free Hardy field. This result relates to classical oscillation criteria for second-order homogeneous linear differential equations.…
Normalizing Asymptotic Differential Equations
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection wit…
Analytic Ax-Kochen-Ersov theory with lifts of the residue field and value group
Neer Bhardwaj, Lou van den Dries
We develop an extension theory for analytic valuation rings in order to establish Ax-Kochen-Ersov type results for these structures. New is that we can add in salient cases lifts o…