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On a Characteristic Feature of the Positive Logics

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono  and
Jiro Ito
Katuzi Ono
Affiliation:
Mathematical Institute, Nagoya University
Jiro Ito
Affiliation:
Mathematical Institute, Nagoya University
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In this short note, we would like to point out that the following property (called ASSUMPTION REMOVABILITY in the present paper) is characteristic of the positive logics, the primitive logic LO, the positive predicate logics LP (intuitionistic) and LQ (classical):

ASSUMPTION REMOVABILITY. If any propositioncan be deduced from some assumptionhaving no primitive notions in common ivith, thenis also provable without any assumption.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 28 , October 1966 , pp. 193 - 196
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Craig, W.: Linear reasoning. A new form of the Her brand-Gen tzen theorem, J. Symb. Log., 22 (1957), 250–268.Google Scholar
[2] Curry, H. B.: Foundations of mathematical logic, New York (1963).Google Scholar
[3] Gentzen, G.: Untersuchungen über das logische Schliessen, Math. Z., 39 (1934;, 176–210, 405–431.Google Scholar
[4] Johansson, I.: Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus, Compositio Math., 4 (1936), 119–136.Google Scholar
[5] Lorenzen, P.: Einführung in die operative Logik und Mathematik, Berlin-Göttingen-Heidelberg, (1955).Google Scholar
[6] Ono, K.: On universal character of the primitive logic, Nagpya Math. J., 27-1 (1966), 331–353.Google Scholar
[7] Schütte, K.: Der Interpolationssatz der intuitionistischen Prädikatenlogik, Math. Ann., 148 (1962), 192–200.Google Scholar