No 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.

In this paper we prove the strong normalization theorem for second order classical natural deduction. The method used is an adaptation of the one of reducibility candidates introduced in [3] for second order intuitionistic natural deduction. The extension to the classical case requires in particular a simplification of the notion of reducibility candidate.