8 papers
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…
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…
Revisiting second-order linear differential equations over Hardy fields
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We review second-order homogeneous linear differential equations with coefficient functions whose germs lie in a Hardy field (and hence are strongly non-oscillating). We prove a co…
Extending Fubini Measures
Lou van den Dries
Let be stably embedded in a structure $\cM=(M;\dots)$. We consider {\em Fubini measures} on the subcategory $\Def(C)$ of the category $\Def(\cM)$ of definable sets i…
Truncation Structures
Lou van den Dries
We characterize intrinsically the truncation structures on valued fields arising from embeddings into Hahn fields with truncation closed image.
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…