Lecture Notes in Logic, 25

Nonstandard Methods and Applications in Mathematics

Nigel J. Cultand, Mauro Di Nasso, David A. Ross , editors

Year: 2006
262 pages. Hardcover.

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A collection of research articles that arose from a conference on Nonstandard Analysis and Applications in Mathematics held in Pisa, Italy, June 2002. The papers are a mix of survey articles and research articles. They cover the foundations of nonstandard analysis, nonstandard analysis in pure mathematics and in applied mathematics, and even teaching calculus with nonstandard analysis.

Table of Contents

  • Preface


  • Vieri Benci, Mauro Di Nasso, and Marco Forti
    The eightfold path to nonstandard analysis
  • Sergio Fajardo and H. Jerome Keisler
    Neoclosed forcing
  • Karel Hrbacek
    Nonstandard objects in set theory

Pure Mathematics 

  • Peter A. Loeb
    The microscopic behavior of measurable functions
  • David A. Ross
    Nonstandard measure contructions—solutions and problems
  • Renling Jin
    Inverse problem for upper asymptotic density II
  • Angus Macintyre
    Nonstandard analysis and cohomology

Applied Mathematics

  • Niegel J. Cutland
    Loeb space methods for stochastic Navier-Stokes equations
  • Manfred P.H. Wolff
    Discrete approximations of compact operators and approximations of their spectra
  • Richard O’Donovan and John Kimber
    Nonstandard analysis at pre-university level: Naive magnitude analysis