Karagila, A orcid.org/0000-0003-1289-0904 and Schweber, N (2022) Choiceless chain conditions. European Journal of Mathematics, 8 (Suppl 2). pp. 393-410. ISSN 2199-675X
Abstract
Chain conditions are one of the major tools used in the theory of forcing. We say that a partial order has the countable chain condition if every antichain (in the sense of forcing) is countable. Without the axiom of choice antichains tend to be of little use, for various reasons, and in this short note we study a number of conditions which in ZFC are equivalent to the countable chain condition.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Axiom of choice; Countable chain condition; Forcing; Symmetric extensions |
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) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 Jul 2022 08:42 |
Last Modified: | 11 Mar 2023 07:12 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s40879-022-00564-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:188477 |