On the Craig-Lyndon interpolation theorem1 | The Journal of Symbolic Logic | Cambridge Core (original) (raw)

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

Copyright

Copyright © Association for Symbolic Logic 1968

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