Basics of non-standard analysis (according to Nelson)

In the analysis, calculating with in?nitesimalen sizes is formalized by the Grenzwertbegri?. Robinson has extended the body of real numbers so that it contains in?nitesimale elements, i.e. positive numbers that are smaller than all positive real numbers. Nelson later observed that the axioms of set theory can be expanded so that the "usual body" of the real numbers "standard" and "non-standard elements". Among the non-standard elements ?nden are again those that are positive and smaller than all positive standard elements.

The proseminar will discuss how the basic statements of the analysis can be reformulated and proven with the help of the in?nitesimalen elements. The proseminar is divided into the following sections:

I. Logical basis of NSA

II. Analysis I in the language of the NSA

III. advanced applications of NSA

IV. A look at Robinson's NSA

Homepage Prof. Schmitt

[1]    D. Landers, L. Rogge, Nichtstandard Analysis, Springer-Lehrbuch, Springer-Verlag, Berlin, 1994, x+485 S.
[2]    A.M. Robert, Nonstandard analysis, revised reprint of the 1988 translation, Dover Publications, Inc., Mineola, NY, 2003, xx+156 S.
[3]    H.-P. Tuschik, H. Wolter, Mathematische Logik—kurzgefaßt. Grundlagen, Modelltheorie, Entscheidbarkeit, Mengenlehre., 2. Au?., Spektrum Hochschultaschenbuch, Spektrum Akademischer Verlag, Heidelberg, 2002, viii+214 S.

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