Jump to ContentJump to Main Navigation
Asymptotic Differential Algebra and Model Theory of Transseries$
Users without a subscription are not able to see the full content.

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

Print publication date: 2017

Print ISBN-13: 9780691175423

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691175423.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2017. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see http://www.universitypressscholarship.com/page/privacy-policy).date: 16 January 2018

Differential-Henselian Fields with Many Constants

Differential-Henselian Fields with Many Constants

Chapter:
(p.365) Chapter Eight Differential-Henselian Fields with Many Constants
Source:
Asymptotic Differential Algebra and Model Theory of Transseries
Author(s):

Matthias Aschenbrenner

Lou van den Dries

Joris van der Hoeven

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691175423.003.0009

This chapter considers differential-henselian fields with many constants. Here d-henselian includes having small derivation, so d-henselian valued differential fields with many constants are monotone. The goal here is to derive Scanlon's extension in [382, 383] of the Ax-Kochen-Eršov theorems to d-henselian valued differential fields with many constants. Among the results to be established is Theorem 8.0.1: Suppose K and L are d-henselian valued differential fields with many constants. Then K = L as valued differential fields if and only if res K = res L as differential fields and Γ‎ subscript K = Γ‎ subscript L as ordered abelian groups. The chapter also discusses an angular component map on K, equivalence over substructures, relative quantifier elimination, and a model companion.

Keywords:   differential-henselian field, constant, valued differential field, Scanlon's extension, ordered abelian group, angular component map, equivalence, substructure, quantifier elimination, model companion

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.