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An addendum

Published online by Cambridge University Press:  12 March 2014

S. C. Kleene
S. C. Kleene*
Affiliation:
The University of Wisconsin
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Extract

This addendum supplies details of the proof in 3.6 of our paper Disjunction and existence under implication in elementary intuition-istic formalisms in this Journal, vol. 27 (1962), pp. 11–18, as promised in Footnote 8 of that paper (p. 16 lines 11 and 16, for “├” read “|”).

A congruence-substitution (or free substitution with change of bound variables) on a formula E with result F consists in, simultaneously, substituting for each of the free variables of E in all its free occurrences a respective term and replacing each bound occurrence of a variable in E by a respective variable, so that (a) each image in F of a free occurrence of a variable in E is free (IM p. 410) and (b) each image in F of a bound occurrence of a variable in E is bound by the corresponding quantifier (i.e. if the j-th quantifier in E binds the original occurrence, then the j-th quantifier in F binds the image).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 28 , Issue 2 , June 1963 , pp. 154 - 156
Copyright
Copyright © Association for Symbolic Logic 1964

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