文档介绍：NON-STANDARD
ANALYSIS
ABRAHAM ROBINSON
University of California, Los Angeles
I966
NO RTH- H 0 L LAN D PUBLISH ING C 0 M PANY
AMSTERDAM
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To Rede
PREFACE
Je vois plus que jamais qu'il ne faut
juger de rien sur sa grandeur apparente.
0 Dieu !qui avez donne' une intelligence
d des substances qui pamissent si
meprisables, I'infiniment petit vous
coiite autant que l'injiniment grand.
VOLTAIRE,Micromegas
In the fall of 1960 it occurred to me that the concepts and methods of
contemporary Mathematical Logic are capable of providing a suitable
framework for the development of the Differential and Integral Calculus
by means of infinitely small and infinitely large numbers. I first reported
my ideas in a seminar talk at Princeton University (November 1960) and,
later, in an address at the annual meeting of the Association for Symbolic
Logic (January 1961) and in a paper published in the Proceedings of the
Royal Academy of Sciences of Amsterdam (ROBINSON [1961]). The re-
sulting subject was called by me Non-standard Analysis since it involves
and was, in part, inspired by the so-called Non-standard models of
Arithmetic whose existence was first pointed out by T. Skolem.
In the intervening years, Non-standard Analysis has developed con-
siderably in several directions. Since many of the results have been
reported so far only in courses or lectures, and in mimeographed reports,
it was thought that a book dedicated entirely to this subject would be
in order,
Over the years, my thinking in this area has been enlivened by dis-
cussions with several colleagues, among whom I venture to mention here
R. Arens, . Chang, A. Erdelyi, A. Horn, G. Kreisel, I. Lakatos, and
J. B. Rosser. Special thanks are due to W. A. J. Luxemburg, whoselectures
an