Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2025-01-03T17:03:19.764Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Craig-Lyndon interpolation theorem1

Published online by Cambridge University Press:  12 March 2014

Arnold Oberschelp
Arnold Oberschelp*
Affiliation:
Universität Kiel
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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