An Introduction to General Nonstandard Analysis

  • Peter A. Loeb
Part of the Mathematics and Its Applications book series (MAIA, volume 510)


In this chapter, we develop the general framework of nonstandard analysis and the necessary logic for the transfer principle. The reader who has read the first chapter of this book will appreciate that Skolem functions will no longer be needed to replace the existential quantifier. The results obtained in the last chapter using our simple transfer principle will still be valid, since the transfer principle used here extends that simple one. The outline of this chapter is similar to that of Chapter 2 of the author’s book with Albert E. Hurd, [4].


Nonstandard Analysis Transfer Principle Elementary Chain Elementary Limit Elementary Embedding 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Peter A. Loeb
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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