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Preprint Number 1432
1432. Nigel Pynn-Coates Differential-henselianity and maximality of asymptotic valued differential fields E-mail: Submission date: 15 May 2018 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. Mathematics Subject Classification: Keywords and phrases: |
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