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On Formal Theories

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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The main purpose of the present paper is to introduce a new understanding of formal theories.

It has been a traditional pattern of formal theories to presuppose a logic and an axiom system for each formal theory. The axiom system of any formal theory consists of a finite number of axiom schemata in general, but occasionally it can be regarded as consisting of a finite number of axioms. I will call any formal theory of this kind an axiomatic theory or an axiom-schematic theory according as its axiom system is regarded as consisting of a finite number of axioms or as consisting of a finite number of axiom schemata.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 361 - 371
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Ono, K.: On universal character of the primitive logic, Nagoya Math. J., 27 (1966), 331–353.Google Scholar
[2] Ono, K.: Reduction of logics to the primitive logic, J. of Math. Soc. Jap., 19–3 (1967), 384–398.Google Scholar
[3] Ono, K.: Taboo versus axiom, Nagoya Math. J., 28 (1966), 73–77.Google Scholar