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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
[2] Ackermann, Wilhelm, Widerspruchsfreier Aufbau der Logik I, this Journal , Vol. 15 (1950), pp. 33–57.Google Scholar
[3] Harrop, R., An investigation of the prepositional calculus used in a particular system of logic, Proceedings of the Cambridge Philosophical Society, Vol. 50 (1954), pp. 495–512.CrossRefGoogle Scholar
[4] McKinsey, J. C. C., A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology, this Journal , Vol. 6 (1941), pp. 117–134.Google Scholar
[5] Padoa, A., Essai d'une théorie algébraique des nombres entiers, précédé d'une introduction logique à une théorie deductive quelconque, Bibliothèque du Congrès International de Philosophie, Vol. 3 (1901), pp. 309–365.Google Scholar
[6] Heyting, A., Die formalen Regeln der intuitionistischen Logik, Sitzungsberichte der Preusslschen Akademie der Wissenschaften, Physikalisch-mate-matische Klasse, 1930, pp. 42–56.Google Scholar
[7] Jaskowski, S., Recherches sur le système de la logique intuitioniste, Actes du Congrès International de Philosophie Scientifique, Paris 1935, part VI, pp. 58–61.Google Scholar
[8] Suszko, Roman, W sprawie logiki bez aksjomatów, Kwartalnik fllosoficzny, Vol. 17 (1948), pp. 199–205.Google Scholar