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arXiv · 1805.01423

Newtonian valued differential fields with arbitrary value group

Nigel Pynn-Coates
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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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BibTeXRIS

Nigel Pynn-Coates. 2018-05-03. Newtonian valued differential fields with arbitrary value group. https://doi.org/10.1080/00927872.2018.1539173

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