Abstract
The purpose of this article is to establish the relation between the new concepts ofΠ 12 -Logic, introduced by Girard [G4] and the traditional approach of cut elimination, in particular with respect to the bounds obtained: The bounds for the cut elimination theorem are given explicitly in the form of dilators. In particular, the bound obtained in the final theorem is the bilatorV, which is a functorial version of the Veblen hierarchy employed in the classical case.
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References
Feferman, S.: Proceedings of the Summer School in Logic — Leeds 1967. Lectures Notes in Mathematics, Vol. 70, Berlin, Heidelberg, New York: Springer 1968.
Ferbus, M.-C.: Bornes fonctorielles pour l'élimination des coupures, 1982. Thèse de 3ème cycle (Univ. Paris 7).
Girard, J.Y.: Cours de theorie de la démonstration. Paris 1979/80 (unpublished).
Girard, J.Y.:Π 12 -logic. Part 1 (Manuscript unpublished).
Girard, J.Y.:Π 12 -logic. Part 1: Dilators — 1980. Ann. Math. Logic21, 75–219 (1981).
Giard, J.Y.: Proof theory and logical complexity, 1982. Bibliopolis Napoli (to appear).
Girard, J.Y., Vauzeilles, J.: Functors and ordinal notations. I. A functorial construction of the Veblen hierarchy, 1980 (to appear).
Vauzeilles, J.: Interpolation et complétude enβ-logique, 1979. Thèse de 3ème cycle (Univ. Paris 7).
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Ferbus, MC. Functorial bounds for cut elimination inL βω . I. Arch math Logik 24, 141–158 (1984). https://doi.org/10.1007/BF02007146
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DOI: https://doi.org/10.1007/BF02007146