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On the Craig-Lyndon interpolation theorem1

Published online by Cambridge University Press:  12 March 2014

Arnold Oberschelp
Arnold Oberschelp*
Affiliation:
Universität Kiel
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Extract

In his paper [3] Henkin proved for a first order language with identity symbol but without operation symbols the following version of the Craig-Lyndon interpolation theorem:

Theorem 1. If Γ╞Δ then there is a formula θ such that Γ ├Δand

(i) any relation symbol with a positive (negative) occurrence in θ has a positive (negative) occurrence in some formula of Γ.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 2 , 23 July 1968 , pp. 271 - 274
Copyright
Copyright © Association for Symbolic Logic 1968

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Footnotes

1

The result is announced in [6]. It was obtained in fall 1966 and the paper read in the mathematical colloquium at Hannover (Germany) on November 25, 1966.

References

[1]Craig, W., Linear reasoning. A new form of the Herbrand-Gentzen theorem, this Journal, vol. 22 (1957), pp. 250–268.Google Scholar
[2]Craig, W., Three uses of the Herbrand-Gentzen theorem, this Journal, vol. 22 (1957), pp. 269–285.Google Scholar
[3]Henkin, L., An extension of the Craig-Lyndon interpolation theorem, this Journal, vol. 28 (1963), pp. 201–216.Google Scholar
[4]Lyndon, R. C., An interpolation theorem in the predicate calculus, Pacifie Journal of mathematics, vol. 9 (1959), pp. 129–142.CrossRefGoogle Scholar
[5]Lyndon, R. C., Properties preserved under homomorphism, Pacific journal of mathematics, vol. 9 (1959), pp. 143–154.CrossRefGoogle Scholar
[6]Oberschelp, A., On the Craig-Lyndon interpolation theorem, Notices of the American Mathematical Society, vol. 14 (1967), p. 142.Google Scholar