Vol. 308, No. 1, 2020

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Differential-henselianity and maximality of asymptotic valued differential fields

Nigel Pynn-Coates

Vol. 308 (2020), No. 1, 161–205
Abstract

We show that asymptotic (valued differential) fields have unique maximal immediate extensions. Connecting this to differential-henselianity, we prove that any differential-henselian asymptotic field is differential-algebraically maximal, removing the assumption of monotonicity from a theorem of Aschenbrenner, van den Dries, and van der Hoeven. Finally, we use this result to show the existence and uniqueness of differential-henselizations of asymptotic fields.

Keywords
valued differential fields, asymptotic fields, immediate extensions, differential-henselianity, differential Newton diagrams
Mathematical Subject Classification 2010
Primary: 12H05, 12J10
Milestones
Received: 7 August 2018
Revised: 25 March 2020
Accepted: 24 April 2020
Published: 3 December 2020
Authors
Nigel Pynn-Coates
Department of Mathematics
The Ohio State University
Columbus, OH
United States