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Proofs of non-deducibility in intuitionistic functional calculus

Published online by Cambridge University Press:  12 March 2014

Andkzej Mostowski
Andkzej Mostowski*
Affiliation:
University of Warsaw
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Extract

It has been proved by S. C. Kleene and David Nelson that the formula

is intuitionistically non-deducible, i.e., non-deducible within the intuitionistic functional calculus.

The aim of this note is to outline a general method which permits us to establish the intuitionistic non-deducibility of many formulas and in particular of the formula (1).

Type
Articles
Information
The Journal of Symbolic Logic , Volume 13 , Issue 4 , December 1948 , pp. 204 - 207
Copyright
Copyright © Association for Symbolic Logic 1948

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References

1 Kleene, S. C., On the interpretation of intuitionistic number theory, this Journal, vol. 10 (1945), pp. 109–124Google Scholar; see especially the last sentence of §10, p. 117.

2 Birkhoff, Garrett, Lattice theory, New York 1940CrossRefGoogle Scholar. See also McKinsey, J. C. C. and Tarski, A., On closed elements in closure algebras, Annals of mathematics, vol. 47 (1946), pp. 122–162.CrossRefGoogle Scholar

3 See Birkhoff, loc. cit. p. 128, and McKinsey and Tarski, loc. cit., Theorem 1.3.