Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-04T18:21:00.590Z Has data issue: false hasContentIssue false

Interpolation in fragments of intuitionistic propositional logic

Published online by Cambridge University Press:  12 March 2014

Gerard R. Renardel de Lavalette*
Affiliation:
Department of Philosophy, University of Utrecht, 3584 Cs Utrecht, The, Netherlands

Abstract

We show in this paper that all fragments of intuitionistic propositional logic based on a subset of the connectives ∧, ∨, →, ¬ satisfy interpolation. Fragments containing ↔ or ¬¬ are briefly considered.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1989

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.)

References

REFERENCES

[H63] Henkin, L., An extension of the Craig-Lyndon interpolation theorem, this Journal, vol. 28 (1963), pp. 201216.Google Scholar
[KK71] Kreisel, G. and Krivine, J. L., Elements of mathematical logic (model theory), North-Holland, Amsterdam, 1971.Google Scholar
[KK72] Kreisel, G. and Krivine, J. L., Modelltheorie, Springer-Verlag, Berlin, 1972.CrossRefGoogle Scholar
[P85] Porebska, M., Interpolation for fragments of intermediale logics, Bulletin of the Section of Logic, Polish Academy of Sciences, vol. 14 (1985), pp. 7983, and Reports on Mathematical Logic , vol. 21 (1987), pp. 9–14.Google Scholar
[R81] de Lavalette, G. R. Renardel, The interpolation theorem in fragments of logics, Indagationes Mathematicae, vol. 43 (1981), pp. 7186.CrossRefGoogle Scholar
[R86] de Lavalette, G. R. Renardel, Interpolation in a fragment of intuitionistic propositional logic, Logic Group Preprint Series, no. 5, University of Utrecht, Utrecht, 1986.Google Scholar
[S62] Schütte, K., Der Interpolationssatz der intuitionistischen Prädikatenlogik, Mathematische Annalen, vol. 148 (1962), pp. 192200.CrossRefGoogle Scholar
[T75] Takeuti, G., Proof theory, North-Holland, Amsterdam, 1975.Google Scholar
[Z78] Zucker, J. I., Interpolation for fragments of the propositional calculus, preprint ZW 116/78, Mathematisch Centrum, Amsterdam, 1978.Google Scholar