Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-19T10:59:22.700Z Has data issue: false hasContentIssue false
  • English
  • Français

On formulas of one variable in intuitionistic propositional calculus1

Published online by Cambridge University Press:  12 March 2014

Iwao Nishimura
Iwao Nishimura*
Affiliation:
Gifu University, Gifu, Japan
Get access Rights & Permissions [Opens in a new window]

Extract

McKinsey and Tarski [3] described Gödel's proof that the number of Brouwerian-algebraic functions is infinite. They gave an example of a sequence of infinitely many distinct Brouwerian-algebraic functions of one argument, which means that there are infinitely many non-equivalent formulas of one variable in the intuitionistic propositional calculus LJ of Gentzen [1]. However they did not completely characterize such formulas. In § 1 of this note, we define a sequence of basic formulas P∞(X), P0(X), P1(X), … and prove the following theorems.

Type
Articles
Information
The Journal of Symbolic Logic , Volume 25 , Issue 4 , December 1960 , pp. 327 - 331
Copyright
Copyright © Association for Symbolic Logic 1962

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

I wish to express my hearty thanks to Prof. K. Ono and Mr. T. Umezawa for their valuable suggestions and criticisms.

References

[1]Gentzen, G., Untersuchungen über das logische Schliessen, Mathematische Zeitschrift, vol. 39. (1934–1935), pp. 176–210, 445–431.CrossRefGoogle Scholar
[2] K. Gödel, Zum intuitionistischen Aussagenkalkül, Ergebnisse eines mathematischen Kolloquiums, Heft 4 (1931–1932, 1933), p. 40.Google Scholar
[3]McKinsey, J. C. C. and Tarski, A., On closed elements in closure algebra, Annals of Mathematics, vol. 47 (1946), pp. 122–162.CrossRefGoogle Scholar
[4]Mostowski, A., Proofs on non-deducibility in intuitionistic functional calculus, this Journal, vol. 13 (1948), pp. 204–207.Google Scholar
[5]Umezawa, T., Über die Zwischensysteme der Aussagenlogik, Nagoya Mathematical Journal, vol. 9 (1955), pp. 181–187.CrossRefGoogle Scholar
[6]Umezawa, T., On intermediate prepositional logics, this Journal, vol. 24 (1959), pp. 20–36.Google Scholar