3 papers
math.LO2025
Dimension theory for the asymptotic couple of the field of logarithmic transseries
Allen Gehret, Elliot Kaplan, Nigel Pynn-Coates
In this paper we completely characterize all dimension functions on all models of the theory of the asymptotic couple of the field of logarithmic transseries (Dimension…
math.AC2018
Differential-henselianity and maximality of asymptotic valued differential fields
Nigel Pynn-Coates
We show that asymptotic (valued differential) fields have unique maximal immediate extensions. Connecting this to differential-henselianity, we prove that any differential-henselia…
math.AC2018
Newtonian valued differential fields with arbitrary value group
Nigel Pynn-Coates
The notion of newtonianity is central to the study of the ordered differential field of logarithmic-exponential transseries done by Aschenbrenner, van den Dries, and van der Hoeven…