The independence of connectives-Reference-Cited by-同舟云学术

The independence of connectives

Published:1962-12 Issue:4 Volume:27 Page:426-436
ISSN:0022-4812
Container-title:Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

Smiley Timothy

Abstract

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).

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference8 articles.

1. Essai d'une théorie algébraique des nombres entiers;Padoa;précédé d'une introduction logique à une théorie deductive quelconque, Bibliothèque du Congrès International de Philosophie,1901

2. Widerspruchsfreier Aufbau der Logik I;Ackermann;this Journal,1950

3. Die formalen Regeln der intuitionistischen Logik;Heyting;Sitzungsberichte der Preusslschen Akademie der Wissenschaften,1930

4. A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology;McKinsey;this Journal,1941

5. Proof of the independence of the primitive symbols of Heyting's calculus of propositions;McKinsey;this Journal,1939

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