This note shows that the permutation instructions presented by Zardini (2011) for eliminating cuts on universally quantified formulas in the sequent calculus for the noncontractive 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 counterexample 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.

中文翻译：

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关于“Truth without CONTRA(DI)CTION”中消减证明的注释

本说明显示了 Zardini (2011) 提出的置换指令，用于消除非收缩真值理论 IKT 的后续演算中普遍量化公式的削减ω不足。为此，本说明介绍了 IKT 后续演算中的推导ω最后在置换指令无法处理的普遍量化公式上应用 cut。反例是那种没有解决在 IKT 的后续演算中是否可以证明割是可消除的问题ω用另一种策略。