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

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Item Type:	Article
Type of entry:	Secondary publication
Title:	Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness
Language:	English
Date:	12 March 2024
Place of Publication:	Darmstadt
Year of primary publication:	November 2021
Place of primary publication:	Berlin; Heidelberg; New York
Publisher:	Springer
Journal or Publication Title:	Archive for Mathematical Logic
Volume of the journal:	60
Issue Number:	7-8
DOI:	10.26083/tuprints-00023435
Corresponding Links:	Publisher-DOI
Origin:	Secondary publication DeepGreen
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.
Uncontrolled Keywords:	Uniform boundedness principle, Bounded collection principle, Monotone functional interpretation, Bounded functional interpretation, Proof mining
Status:	Publisher's Version
URN:	urn:nbn:de:tuda-tuprints-234356
Classification DDC:	500 Science and mathematics > 510 Mathematics
Divisions:	04 Department of Mathematics > Logic
Date Deposited:	12 Mar 2024 13:29
Last Modified:	12 Mar 2024 13:29
SWORD Depositor:	Deep Green
URI:	https://tuprints.ulb.tu-darmstadt.de/id/eprint/23435
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