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Nonstandard Analysis

book
Language:
Author: Erland Gadde
Url: http://www.sm.luth.se/~gadde/
Format: Ps, Dvi
Category: Analysis
Pages: 113
Clicks: 3023

Description
The purpose of this text is twofold. The first purpose is to develop basic nonstandard analysis by an axiomatic ap-proach. The axiom system we use is a modified version of an axiom system in-troduced by Henson; The second purpose is to define and use our superstructures within ZFC, withouturelements. To do this, we introduce a general type of hierarchy of sets, of whichsuperstructures as well as the von Neumann cumulative hierarchy are special cases.We develop a little theory about such hierarchies, and we define a superstructureas such a hierarchy, satisfying some extra conditions. It is these superstructureswe use to define nonstandard extensions of, using axioms. This is also done in fulltechnical detail.

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