8 citations · 24 across the 14 of their papers we have counts for
17 papers
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…
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…
Revisiting closed asymptotic couples
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
Every discrete definable subset of a closed asymptotic couple with ordered scalar field is shown to be contained in a finite-dimensional -linear subs…
On the Pila-Wilkie theorem
Neer Bhardwaj, Lou van den Dries
This expository paper gives an account of the Pila-Wilkie counting theorem and some of its extensions and generalizations. We use semialgebraic cell decomposition to simplify part…
On the uniqueness of maximal immediate extensions of valued differential fields
Lou van den Dries, Nigel Pynn-Coates
So far there exist just a few results about the uniqueness of maximal immediate valued differential field extensions and about the relationship between differential-algebraic maxim…
Maximal immediate extensions of valued differential fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an ex…
Dimension in the realm of transseries
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
Let be the differential field of transseries. We establish some basic properties of the dimension of a definable subset of , also in relation to its codi…
The surreal numbers as a universal H-field
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We show that the natural embedding of the differential field of transseries into Conway's field of surreal numbers with the Berarducci-Mantova derivation is an elementary embedding…
Asymptotic Differential Algebra and Model Theory of Transseries
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We develop here the algebra of the differential field of transseries and of related valued differential fields. This book contains in particular our recently obtained decisive posi…
Towards a Model Theory for Transseries
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
The differential field of transseries extends the field of real Laurent series, and occurs in various context: asymptotic expansions, analytic vector fields, o-minimal structures,…
Globalizing locally compact local groups
Lou van den Dries, Isaac Goldbring
Every locally compact local group is locally isomorphic to a topological group.
Equivalence of Valued Fields with Valuation Preserving Automorphism
Salih Azgin, Lou van den Dries
We improve results of Belair, Macintyre, and Scanlon on valued fields with a valuation preserving automorphism by weakening their assumptions on the residue difference field. In th…