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Eventual Quantities, Immediate Extensions, and Special Cuts

Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven

in Asymptotic Differential Algebra and Model Theory of Transseries

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691175423
eISBN:
9781400885411
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175423.003.0012
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter deals with eventual quantities, immediate extensions, and special cuts. It first considers the behavior of eventual quantities before discussing Newton weight, Newton degree, and Newton ... More


Newtonian Differential Fields

Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven

in Asymptotic Differential Algebra and Model Theory of Transseries

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691175423
eISBN:
9781400885411
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175423.003.0015
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter deals with Newtonian differential fields. Here K is an ungrounded H-asymptotic field with Γ‎ := v(Ksuperscript x ) not equal to {0}. So the subset ψ‎ of Γ‎ is nonempty and has no largest ... More


Newtonianity of Directed Unions

Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven

in Asymptotic Differential Algebra and Model Theory of Transseries

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691175423
eISBN:
9781400885411
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175423.003.0016
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter considers the newtonianity of directed unions and proves an analogue of Hensel's Lemma for ω‎-free differential-valued fields of H-type: Theorem 15.0.1. Here K is an H-asymptotic field ... More


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