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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
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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

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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