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An extension of the Craig-Lyndon interpolation theorem1

Published online by Cambridge University Press:  12 March 2014

Leon Henkin
Leon Henkin*
Affiliation:
Institute for Advanced Study, and University of California, Berkeley
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Extract

In a work widely quoted and applied,3 Craig has shown that if A and C are any formulas of predicate logic such that A├C, then there is a formula B such that (i) A├B and B├C, and (ii) each predicate symbol occurring in B occurs both in A and in C.4 If, in this theorem, we replace the syntactic notion of derivability, ├, by the semantical notion of consequence, ╞, the resulting proposition is of course equally valid, for by the (strong) completeness theorem of predicate logic5 the relations ├ and ╞ coincide in extension.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 28 , Issue 3 , September 1963 , pp. 201 - 216
Copyright
Copyright © Association for Symbolic Logic 1964

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Footnotes

1

This work was begun while the author served as Visiting Professor at Dartmouth College. Another portion of the work was supported by the National Science Foundation (Grant No. G-14006). A version of the paper was presented at a meeting of the Association for Symbolic Logic on December 27, 1961.

References

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