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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.