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What is nonstandard analysis? (Japanese) Zbl 0633.26010

This paper is a survey on nonstandard analysis. It contains three parts: the frames of nonstandard analysis (I.1-I.5), some applications (II.6- II.9), and nonstandard set theory (III.10). Particularly, some works of Japanese scholars are included.
The goal of I.1 and I.2 is to give the basic concepts as Zermelo’s universes, transfer axiom and enlargement axiom. With these materials it is possible to define infinitesimal numbers. A further discussion (Robinson’s ultrafilter, ultrapower, LOS theorem, internal and external set, saturated model) is given in I.3-I.5. In II.7. the author proves the existence of Haar measure. Perhaps this proof is a new one. The Loeb measure theory which the author describes in II.9 is one of recent results of nonstandard analysis. In the last section, the author deals with a new set theory, Kawai’s NST theory [T. Kawai, Logic, Proc. Southeast Asian Conf., Singapore 1981, Stud. Logic Found. Math. 111, 55- 76 (1983; Zbl 0542.03046)].
Reviewer: Lie-Ren Sheng

MSC:

26E35 Nonstandard analysis
28E05 Nonstandard measure theory
03H05 Nonstandard models in mathematics

Citations:

Zbl 0542.03046
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