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The strong normalization theorem for second-order classical natural deduction is proved. The method used is an adaptation of the one of reducibility candidates introduced in a thesis by J.Y. Girard (Univ. Paris 7, 1972) for second-order intuitionistic natural deduction. The extension to the classical case requires, in particular, a simplification of the notion of reducibility candidates
@InProceedings{Parigot-Strongnormalization,
author = {Michel Parigot},
title = {Strong normalization for second order classical natural deduction },
booktitle = {Proceedings of the Eighth Annual IEEE Symposium on Logic in Computer Science (LICS 1993)},
year = {1993},
month = {June},
pages = {39--46},
location = {Montreal, Canada},
publisher = {IEEE Computer Society Press}
}