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Introduction of a Basic Theory of Objects

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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In constructing various kind of mathematical theories on the basis of a common basic theory, it has been very usual to take up the set theory as the common basic theory. This approach has been already successful to a certain extent and looks like successfully developable in the future not only in constructing mathematical theories standing on the classical logic but also in constructing formal theories standing on weaker logics. In constructing mathematical theories standing on the classical logic, it has been successful in most cases only by interpreting mathematical notions in the set theory without defining any special interpretation of logical notions. In constructing any mathematical theory standing on weaker logics such as the intuitionistic logic, however, we have to give a special interpretation for logical notions, too.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 38 , March 1970 , pp. 185 - 225
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

Literature

[1] Ono, Katuzi; On formal theories, Nagoya Math. J., 32 (1968), 361–371.Google Scholar
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