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A Set Theory Founded on Unique Generating Principle

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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The most important thing for a set theory seems to be that it can generate new mathematical objects, and I think that there must be an underlying principle, simple and unique, which unifies the acts of generating. The naive set theory has a unique generating principle, which defines, by any proposition on a variable x, the set of all x’s satisfying the proposition. Certainly, we must restrict this generating principle so as to exclude all contradictions it contains, without losing its essential rôle as logic of mathematics, and at the same time we would like to keep its uniqueness and simplicity.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957 , pp. 151 - 159
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

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