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Interpolation in fragments of intuitionistic propositional logic

Published online by Cambridge University Press:  12 March 2014

Gerard R. Renardel de Lavalette
Gerard R. Renardel de Lavalette*
Affiliation:
Department of Philosophy, University of Utrecht, 3584 Cs Utrecht, The, Netherlands
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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
Information
The Journal of Symbolic Logic , Volume 54 , Issue 4 , December 1989 , pp. 1419 - 1430
Copyright
Copyright © Association for Symbolic Logic 1989

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References

REFERENCES

[H63] Henkin, L., An extension of the Craig-Lyndon interpolation theorem, this Journal, vol. 28 (1963), pp. 201–216.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. 79–83, 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. 71–86.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. 192–200.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