Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T20:28:59.579Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalization of a lemma of G. F. Rose*

Published online by Cambridge University Press:  12 March 2014

I. L. Gál ,
J. B. Rosser  and
D. Scott
I. L. Gál
Affiliation:
Cornell University and Princeton University
J. B. Rosser
Affiliation:
Cornell University and Princeton University
D. Scott
Affiliation:
Cornell University and Princeton University
Get access Rights & Permissions [Opens in a new window]

Extract

In attempting to reconstruct Rose's proof of Lemma 3.2 of [1], the present authors found what is apparently a different and simpler method, which moreover leads to a far stronger conclusion.

We are operating in the Heyting prepositional calculus as formulated on p. 3 of [1] or on pp. 82 and 101 of [2], and shall make use of relevant theorems on pp. 90, 113–119 of [2]. We shall use a, b, c, w, x, y, z as propositional variables.

We say that a conjunction is simple if each factor has one of the forms: (i) a, (ii) ¬a, (iii) a⊃b, (iv) a⊃(b∨c), (v) (a&b)⊃c, (vi) (a⊃b)⊃c.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 23 , Issue 2 , June 1958 , pp. 137 - 138
Copyright
Copyright © Association for Symbolic Logic 1958

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

*

The preparation of this paper was supported in part by the United States Navy under Contract No. NONR 401(20)–NR 043–167 monitored by the Office of Naval Research.

References

REFERENCES

[1]Rose, G. F., Propositioned calculus and realizability, Transactions of the American Mathematical Society, vol. 75 (1953), pp. 1–19.CrossRefGoogle Scholar
[2]Kleene, S. C., Introduction to Metamathematics, Amsterdam (North Holland), Groningen (Noordhoff), New York and Toronto (Van Nostrand), 1952, x + 550 pp.Google Scholar