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On intermediate propositional logics

Published online by Cambridge University Press:  12 March 2014

Toshio Umezawa
Toshio Umezawa*
Affiliation:
Nagoya University, Nagoya, Japan
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Extract

By intermediate prepositional logics we mean prepositional logics between the intuitionistic and classical logics.

K. Gödel [1] proved that there is a set of intermediate prepositional logics which possesses the order type ω. The method enables us to define intermediate logics in terms of axioms and rules of inference. We shall call it the axiomatic method.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 24 , Issue 1 , March 1959 , pp. 20 - 36
Copyright
Copyright © Association for Symbolic Logic 1959

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References

[1]Gödel, Kurt, Zum intuitionistischen Aussagenkalkül, Ergebnisse eines mathematischen Kolloquiums, Heft 4 (1931–1932, 1933) p. 40.Google Scholar
[2]Rose, Gene F., Propositional calculus and realizability, Transactions of the American Mathematical Society, vol. 75 (1953) pp. 1–19.CrossRefGoogle Scholar
[3]Kleene, S. C., On the interpretation of intuitionistic number theory, this Journal, vol. 10 (1945) pp. 109–124.Google Scholar
[4]Umezawa, T., Über die Zwischensysteme der Aussagenlogik, Nagoya mathematical journal, vol. 9 (1955) pp. 181–189.CrossRefGoogle Scholar
[5]Gentzen, Gerhard, Untersuchungen über das logische Schliessen, Mathematische Zeitschrift, vol. 39 (1934–1945) pp. 176–210, 405–431.CrossRefGoogle Scholar
[6]Maehara, S., Eine Darstellung der intuitionistischen Logik in der klassischen, Nagoya mathematical journal, vol. 7 (1954) pp. 46–64.CrossRefGoogle Scholar
[7]Birkhoff, G., Lattice theory, 2nd ed., New York, 1948.Google Scholar
[8]McKinsey, J. C. C., Proof of the independence of the primitive symbols of Heyting's calculus of propositions, this Journal, vol. 4 (1939) pp. 155–158.Google Scholar
[9]Hilbert, D. and Ackermann, W., Grundzüge der theoretischen Logik, 3rd ed., Springer, 1949.CrossRefGoogle Scholar