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math.LO2024★ 1 cited
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…
math.LO2024
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…
math.LO2023
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…