Kohlenbach, Ulrich (2024)
Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness.
In: Archive for Mathematical Logic, 2021, 60 (7-8)
doi: 10.26083/tuprints-00023435
Article, Secondary publication, Publisher's Version
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URL / URN: https://tuprints.ulb.tu-darmstadt.de/23435
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2024 |
| Creators: | Kohlenbach, Ulrich |
| 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 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/23435 |
| Corresponding Links: | |
| 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 04 Department of Mathematics > Logic |
| Date Deposited: | 12 Mar 2024 13:29 |
| Last Modified: | 19 Mar 2024 10:35 |
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| Suche nach Titel in: | TUfind oder in Google |
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