11 citations · 26 across the 8 of their papers we have counts for
4 papers · 1 filter
On a Differential Intermediate Value Property
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
Liouville closed -fields are ordered differential fields whose ordering and derivation interact in a natural way and where every linear differential equation of order has a…
Hardy fields, the intermediate value property, and -freeness
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
We discuss the conjecture that every maximal Hardy field has the Intermediate Value Property for differential polynomials, and its equivalence to the statement that all maximal Har…
Logarithmic Hyperseries
Lou van den Dries, Joris van der Hoeven, Elliot Kaplan
We define the field of logarithmic hyperseries, construct on natural operations of differentiation, integration, and composition, establish the basic prop…
On numbers, germs, and transseries
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven
Germs of real-valued functions, surreal numbers, and transseries are three ways to enrich the real continuum by infinitesimal and infinite quantities. Each of these comes with natu…