The Computational Content of Arithmetical Proofs

Notre Dame Journal of Formal Logic 53 (3):289-296 (2012)
For any extension $T$ of $I\Sigma_{1}$ having a cut-elimination property extending that of $I\Sigma_{1}$ , the number of different proofs that can be obtained by cut elimination from a single $T$ -proof cannot be bound by a function which is provably total in $T$.
Keywords computational content   cut elimination   first-order arithmetic
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DOI 10.1215/00294527-1716811
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