In Barrio et al. (Forthcoming) Barrio Pailos and Szmuc prove that there are systems of logic that agree with classical logic up to any finite meta-inferential level, and disagree with it thereafter. This article presents a generalized sense of meta-inference that extends into the transfinite, and proves analogous results to all transfinite orders.

中文翻译：

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超限元推理

在巴里奥等人。（即将出版）Barrio Pailos 和 Szmuc 证明存在逻辑系统在任何有限元推理级别都与经典逻辑一致，之后不同意。本文介绍了扩展到超限的元推理的广义意义，并​​证明了所有超限阶次的类似结果。