Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness

Archive for Mathematical Logic 60 (7):995-1003 (2021)
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Abstract

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.

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10.1007/s00153-021-00771-w

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Bounded functional interpretation.Fernando Ferreira & Paulo Oliva - 2005 - Annals of Pure and Applied Logic 135 (1):73-112.

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