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This article is available for purchase or by subscription. See below.
Abstract
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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.
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Keywords
valued differential fields, asymptotic fields, immediate
extensions, differential-henselianity, differential Newton
diagrams
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Mathematical Subject Classification 2010
Primary: 12H05, 12J10
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Milestones
Received: 7 August 2018
Revised: 25 March 2020
Accepted: 24 April 2020
Published: 3 December 2020
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