Proofs of strong normalisation for second order classical natural deduction

Journal of Symbolic Logic 62 (4):1461-1479 (1997)
Abstract We give two proofs of strong normalisation for second order classical natural deduction. The first one is an adaptation of the method of reducibility candidates introduced in [9] for second order intuitionistic natural deduction; the extension to the classical case requires in particular a simplification of the notion of reducibility candidate. The second one is a reduction to the intuitionistic case, using a Kolmogorov translation
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