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On an Application of Intermediate Logics

Published online by Cambridge University Press:  22 January 2016

Toshio Umezawa
Toshio Umezawa*
Affiliation:
Mathematical Institute, Nagoya University
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In [1] I investigated some logics intermediate between intuitionistic and classical predicate logics. The purpose of this paper is to show the possibility of applying some intermediate logics to mathematics namely, to show that some mathematical theorems which are provable in the classical logic but not provable in the intuitionistic logic are provable in some intermediate logics. Let LZ be the logical system obtained from LJ′ a variant of Gentzen’s LJ [2], by adding as axioms all those sequents which can be obtained from a sequent scheme Z by substitution for propositional, predicate, or individual variables.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 16 , February 1960 , pp. 119 - 133
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

[1] Umezawa, T., On logics intermediate between intuitionistic and classical predicate logics. J. Symbolic Logic 24 (1959), forthcoming.Google Scholar
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