Karagila, A. orcid.org/0000-0003-1289-0904 and Ryan-Smith, C. (2024) Which pairs of cardinals can be Hartogs and Lindenbaum numbers of a set? Fundamenta Mathematicae, 267 (3). pp. 231-241. ISSN 0016-2736
Abstract
Given any λ ≼ κ, we construct a symmetric extension in which there is a set X such that ℵ(X) = λ and ℵ<sup>∗</sup>(X) = κ. Consequently, we show that ZF + “for all pairs of infinite cardinals λ ≼ κ there is a set X such that ℵ(X) = λ ≼ κ = ℵ<sup>∗</sup>(X)” is consistent.
Metadata
| Item Type: | Article |
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| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | This is an author produced version of an article accepted for publication in Fundamenta Mathematicae. Uploaded in accordance with the publisher's self-archiving policy. |
| Dates: |
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| Institution: | The University of Leeds |
| Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
| Depositing User: | Symplectic Publications |
| Date Deposited: | 18 Jun 2025 10:58 |
| Last Modified: | 18 Jun 2025 11:34 |
| Status: | Published |
| Publisher: | Institute of Mathematics |
| Identification Number: | 10.4064/fm231006-14-8 |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:227949 |

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