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A Theory of Mathematical Objects as a Prototype of Set Theory

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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The theory of mathematical objects, developed in this work, is a trial system intended to be a prototype of set theory. It concerns, with respect to the only one primitive notion “proto-membership”, with a field of mathematical objects which we shall hereafter simply call objects, it is a very simple system, because it assumes only one axiom scheme which is formally similar to the aussonderung axiom of set theory. We shall show that in our object theory we can construct a theory of sets which is stronger than the Zermelo set-theory [1] without the axiom of choice.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 20 , June 1962 , pp. 105 - 168
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1962

References

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