In this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use of countable Heine–Borel compactness.

中文翻译：

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证明理论上的一致有界性和有界集合原理以及可数的Heine-Borel紧性

在本注释中，我们证明了允许理论上证明使用抽象度量结构对可数Heine-Borel紧缩性的某些实例进行形式化的证明理论统一有界或有界集合原理，必须与不受限制地使用可数Heine-Borel紧致性加以区别。