5 citations · 10 across the 8 of their papers we have counts for
8 papers
Dimension and topology in transserial tame pairs
Nigel Pynn-Coates
Every maximal Hardy field has a proper elementary differential subfield that is Dedekind complete in the maximal Hardy field. This pair of Hardy fields is a transserial tame pair,…
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…
Tame pairs of transseries fields
Nigel Pynn-Coates
This paper concerns pairs of models of the theory of the differential field of logarithmic-exponential transseries that are tame as a pair of real closed fields. That is, the small…
Monotone -convex -differential fields
Elliot Kaplan, Nigel Pynn-Coates
Let be a complete, model complete o-minimal theory extending the theory of real closed ordered fields and assume that is power bounded. Let be a model of equipped w…
Model theory of differential-henselian pre--fields
Nigel Pynn-Coates
Pre--fields are ordered valued differential fields satisfying some basic axioms coming from transseries and Hardy fields. We study pre--fields that are differential-Hensel-Li…
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…
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…
On the uniqueness of maximal immediate extensions of valued differential fields
Lou van den Dries, Nigel Pynn-Coates
So far there exist just a few results about the uniqueness of maximal immediate valued differential field extensions and about the relationship between differential-algebraic maxim…