16 citations · 59 across the 20 of their papers we have counts for
11 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…
Surreal numbers as hyperseries
Vincent Bagayoko, Joris van der Hoeven
Surreal numbers form the ultimate extension of the field of real numbers with infinitely large and small quantities and in particular with all ordinal numbers. Hyperseries can be r…
The hyperserial field of surreal numbers
Vincent Bagayoko, Joris van der Hoeven
For any ordinal , we show how to define a hyperexponential and a hyperlogarithm on the class of positive infinitely large surreal…
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.
Surreal substructures
Vincent Bagayoko, Joris van der Hoeven
Conway's field No of surreal numbers comes both with a natural total order and an additional "simplicity relation" which is also a partial order. Considering No as a doubly ordered…
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…
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,…