[FOM] Computational Nonstandard Analysis

[John Baldwin]

On Tue, September 1, 2015 08:26, Harvey Friedman wrote:
> Thanks! So A. Robinson used the compactness route and Luxembourg the
> ultra power route? Might be convenient to have you mention a readable
> history of nonstandard analysis for people who don't work in it, like
> me and most subscribers.

Mikhail Katz replied in part

>In 1977 Edward Nelson provided an axiomatisation of Robinson's
>framework called Internal Set Theory (IST) which can be thought of as
>a syntactic approach to NSA.  Karel Hrbacek independently developed a
>syntactic axiomatisation at about the same time.

I extend the history a bit with further references
A text based on Hrbacek'  approach  and designed for high school and
college use has recently appeared.

Analysis with Ultrasmall Numbers (Textbooks in Mathematics) 1st Edition
by Karel Hrbacek
<http://www.amazon.com/Karel-Hrbacek/e/B00QJ0UQ3Q/ref=dp_byline_cont_book_1>
  (Author), Olivier Lessmann
<http://www.amazon.com/Olivier-Lessmann/e/B00MS5IWNW/ref=dp_byline_cont_book_2>
  (Author), Richard O'Donovan
<http://www.amazon.com/Richard-ODonovan/e/B00MS5IW78/ref=dp_byline_cont_book_3>
  (Author)

http://www.amazon.com/Analysis-Ultrasmall-Numbers-Textbooks-Mathematics/dp/1498702651

It has been used successfully in the Geneva schools.

There is a summary of the approach in the Math Monthly

http://www.jstor.org/stable/10.4169/000298910X521661?seq=1#page_scan_tab_contents

John T. Baldwin
Professor Emeritus
Department of Mathematics, Statistics,
and Computer Science M/C 249
jbaldwin at uic.edu
851 S. Morgan
Chicago IL
60607
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