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arXiv · 1805.05890

Differential-henselianity and maximality of asymptotic valued differential fields

Nigel Pynn-Coates
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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 (arXiv:1509.02588, Theorem 7.0.3). Finally, we use this result to show the existence and uniqueness of differential-henselizations of asymptotic fields.

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Nigel Pynn-Coates. 2018-05-15. Differential-henselianity and maximality of asymptotic valued differential fields. https://doi.org/10.2140/pjm.2020.308.161

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