Archive for Mathematical Logic 55 (3-4):461-473 (2016)

Sara Negri
University of Helsinki
In 1968, Orevkov presented proofs of conservativity of classical over intuitionistic and minimal predicate logic with equality for seven classes of sequents, what are known as Glivenko classes. The proofs of these results, important in the literature on the constructive content of classical theories, have remained somehow cryptic. In this paper, direct proofs for more general extensions are given for each class by exploiting the structural properties of G3 sequent calculi; for five of the seven classes the results are strengthened to height-preserving statements, and it is further shown that the constructive and minimal proofs are identical in structure to the classical proof from which they are obtained.
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DOI 10.1007/s00153-016-0474-y
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References found in this work BETA

Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.
Structural Proof Theory.Harold T. Hodes - 2006 - Philosophical Review 115 (2):255-258.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
Basic Proof Theory.Roy Dyckhoff - 2001 - Bulletin of Symbolic Logic 7 (2):280-280.

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