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Preprint Number 1421

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1421. Nigel Pynn-Coates
Newtonian valued differential fields with arbitrary value group
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Submission date: 3 May 2018

Abstract:

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; see Chapter 14 of arxiv:1509.02588. We remove the assumption of divisible value group from two of their results concerning newtonianity, namely the newtonization construction and the equivalence of newtonianity with asymptotic differential-algebraic maximality. We deduce the uniqueness of immediate differentially algebraic extensions that are asymptotically differential-algebraically maximal.

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Full text arXiv 1805.01423: pdf, ps.


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