The strength of countable saturation
| dc.contributor.author | van den Berg, Benno | |
| dc.contributor.author | Briseid, Eyvind Martol | |
| dc.contributor.author | Safarik, Pavol | |
| dc.date.accessioned | 2017-10-30T17:19:08Z | |
| dc.date.accessioned | 2018-01-08T12:31:22Z | |
| dc.date.available | 2017-10-30T17:19:08Z | |
| dc.date.available | 2018-01-08T12:31:22Z | |
| dc.date.issued | 2017 | |
| dc.identifier.citation | van den Berg B, Briseid E, Safarik P. The strength of countable saturation. Archive for mathematical logic. 2017;56(5-6):699-711 | en |
| dc.identifier.issn | 0933-5846 | |
| dc.identifier.issn | 1432-0665 | |
| dc.identifier.uri | https://hdl.handle.net/10642/5448 | |
| dc.description.abstract | In earlier work we introduced two systems for nonstandard analysis, one based on classical and one based on intuitionistic logic; these systems were conservative extensions of first-order Peano and Heyting arithmetic, respectively. In this paper we study how adding the principle of countable saturation to these systems affects their proof-theoretic strength. We will show that adding countable saturation to our intuitionistic system does not increase its proof-theoretic strength, while adding it to the classical system increases the strength from first- to full second-order arithmetic. | en |
| dc.language.iso | en | en |
| dc.publisher | Springer | en |
| dc.rights | © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0 | |
| dc.subject | Proof theory | en |
| dc.subject | Arithmetic | en |
| dc.subject | Saturation principles | en |
| dc.title | The strength of countable saturation | en |
| dc.type | Journal article | en |
| dc.type | Peer reviewed | en |
| dc.date.updated | 2017-10-30T17:19:08Z | |
| dc.description.version | publishedVersion | en |
| dc.identifier.doi | http://doi.org/10.1007/s00153-017-0567-2 | |
| dc.identifier.cristin | 1508712 | |
| dc.source.journal | Archive for mathematical logic | |
| dc.relation.projectID | Norges forskningsråd: 204762 |
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This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.