Asymptotic Differential Algebra and Model Theory of Transseries /

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logar...

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Bibliographische Detailangaben
Hauptverfasser: Aschenbrenner, Matthias (VerfasserIn), van den Dries, Lou (VerfasserIn), van der Hoeven, Joris (VerfasserIn)
Format: E-Book
Sprache:Englisch
Veröffentlicht: Princeton, NJ : Princeton University Press, 2017
Schriftenreihe:Annals of Mathematics Studies ; 358
Schlagworte:
MATHEMATICS / Algebra / Abstract.
algebra
matematika
ISBN:9781400885411
Online-Zugang: Volltext
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Inhaltsangabe:
  • Frontmatter
  • Contents
  • Preface
  • Conventions and Notations
  • Leitfaden
  • Dramatis Personæ
  • Introduction and Overview
  • Chapter One. Some Commutative Algebra
  • Chapter Two. Valued Abelian Groups
  • Chapter Three. Valued Fields
  • Chapter Four. Differential Polynomials
  • Chapter Five. Linear Differential Polynomials
  • Chapter Six. Valued Differential Fields
  • Chapter Seven. Differential-Henselian Fields
  • Chapter Eight. Differential-Henselian Fields with Many Constants
  • Chapter Nine. Asymptotic Fields and Asymptotic Couples
  • Chapter Ten. H-Fields
  • Chapter Eleven. Eventual Quantities, Immediate Extensions, and Special Cuts
  • Chapter Twelve. Triangular Automorphisms
  • Chapter Thirteen. The Newton Polynomial
  • Chapter Fourteen. Newtonian Differential Fields
  • Chapter Fifteen. Newtonianity of Directed Unions
  • Chapter Sixteen. Quantifier Elimination
  • Appendix A. Transseries
  • Appendix B. Basic Model Theory
  • Bibliography
  • List of Symbols
  • Index

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