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The independence of connectives

Published online by Cambridge University Press:  12 March 2014

Timothy Smiley
Timothy Smiley*
Affiliation:
University of Cambridge
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Extract

In a paper in this Journal [1], McKinsey used as a criterion for the independence (non-definability) of a connective F in a propositional calculus L, the existence of a matrix for L in which the functions corresponding to all the connectives other than F are class-closing over some subset S of the elements, while the function corresponding to F is not class-closing over S (i.e., for a certain choice of arguments in S its value is not in S).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 27 , Issue 4 , December 1962 , pp. 426 - 436
Copyright
Copyright © Association for Symbolic Logic 1962

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References

[1] McKinsey, J. C. C., Proof of the independence of the primitive symbols of Heyting's calculus of propositions, this Journal , Vol. 4 (1939), pp. 155–158.Google Scholar
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