A note on the cut-elimination proof in "truth without contra(di)ction"
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This note shows that the permutation instructions presented by Zardini in "Truth without contra(di)ction" (RSL, 2011) for eliminating cuts on universally quantified formulas in the sequent calculus for the non-contractive theory of truth IKTω are inadequate. To that purpose the note presents a derivation in the sequent calculus for IKTω ending with an application of cut on a universally quantified formula which the permutation instructions cannot deal with. The counter-example is of the kind that leaves open the question whether cut can be shown to be eliminable in the sequent calculus for IKTω with an alternative strategy.
CitationFjellstad. A note on the cut-elimination proof in "truth without contra(di)ction". The Review of Symbolic Logic. 2019
PublisherCambridge University Press
Copyright Association for Symbolic Logic, 2019