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A propositional calculus with denumerable matrix

Published online by Cambridge University Press:  12 March 2014

Michael Dummett
Michael Dummett*
Affiliation:
Oxford University
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Extract

§1. In [1] Gödel proves the non-existence of a finite matrix characteristic for the intuitionist propositional calculus IC by the use of the finite matrices , where n is a natural number and

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 24 , Issue 2 , June 1959 , pp. 97 - 106
Copyright
Copyright © Association for Symbolic Logic 1959

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References

[1]Gödel, K., Zum iniuitionistischen Aussagenkalkül, Ergebnisse eines mathematischen Kolloquiums, Heft IV (for 1931–32, pub. 1933), p. 40.Google Scholar
[2]McKinsey, J. C. C. and Tarski, A., Some theorems about the sentential calculi of Lewis and Heyting, this Journal, vol. 13 (1948), pp. 1–15.Google Scholar
[3]Jaśkowski, S., Recherches sur le système de la logique intuitioniste, Actes du Congrès International de Philosophie Scientifique, VI Philosophie des mathématiques, Paris (Hermann & Cie.) 1936, pp. 58–61.Google Scholar
[4]Rose, G. F., Propositional calculus and realizability, Transactions of the American Mathematical Society, vol. 75 (1953), pp. 1–19.CrossRefGoogle Scholar
[5]Kleene, S. C., Introduction to metamathematics, Amsterdam (North Holland), Groningen (Noordhoff), New York and Toronto (Van Nostrand) 1952, x + 550 pp.Google Scholar