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: 21 January 2018

Quantifier Elimination

Quantifier Elimination

Chapter:
(p.678) Chapter Sixteen Quantifier Elimination
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/9780691175423.003.0017

This chapter considers the theory Tsuperscript nl of ω‎-free newtonian Liouville closed H-fields that eliminates quantifiers in a certain natural language. This theory has two completions: in the first, the models are the models of Tsuperscript nl with small derivation; in the second, the derivation is not small. One can move from models of the first completion to models of the second completion by compositional conjugation. The chapter begins with a discussion of extensions controlled by asymptotic couples and then shows the uniqueness-up-to-isomorphism of Newton-Liouville closures of ω‎-free H-fields. It then constructs a ω‎-free ΔΩ‎-field extension of K with a useful semiuniversal property. It also deduces Theorem 7 about quantifier elimination with various interesting consequences and concludes by specifying the language of ΔΩ‎-fields and demonstrating the elimination of quantifiers with applications.

Keywords:   quantifier elimination, Liouville closed H-field, small derivation, compositional conjugation, extension, asymptotic couple, Newton-Liouville closure

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.