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Bounds on transfer principles for algebraically closed and complete discretely valued fields

About this Title

Scott Shorey Brown

Publication: Memoirs of the American Mathematical Society
Publication Year: 1978; Volume 15, Number 204
ISBNs: 978-0-8218-2204-3 (print); 978-1-4704-0302-7 (online)
DOI: https://doi.org/10.1090/memo/0204
MathSciNet review: 494980
MSC: Primary 03C60; Secondary 12L05

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Table of Contents

Chapters

  • I. Introduction
  • II. Prerequisites in logic
  • III. Methods for limitation of quantifiers
  • IV. Additive rational numbers
  • V. Additive integers
  • VI. Projection of a set of polynomials
  • VII. Real numbers
  • VIII. Valued fields
  • IX. Algebraically closed fields
  • X. Convergent power series over complete algebraically closed valued fields
  • XI. Hensel’s lemma
  • XII. Convergence of series solutions of polynomials
  • XIII. Complete discretely valued fields with residue class field $Z_p$ and $p$ large
  • XIV. Applications to the Ax-Kochen transfer principle and the Artin conjecture