Karagila, A. orcid.org/0000-0003-1289-0904 and Schilhan, J. (2024) Geometric Condition for Dependent Choice. Acta Mathematica Hungarica, 172 (1). pp. 34-41. ISSN 0236-5294
Abstract
We provide a geometric condition which characterises when the Principle of Dependent Choice holds in a Fraenkel-Mostowski-Specker permutation model. This condition is a slight weakening of requiring the filter of groups to be closed under countable intersections. We show that this condition holds nontrivially in a new permutation model we call "the nowhere dense model" and we study its extensions to uncountable cardinals as well.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Author(s). 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: | permutation model; dependent choice; shift completeness |
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) |
Funding Information: | Funder Grant number MRC (Medical Research Council) MR/T021705/2 |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Jan 2024 16:46 |
Last Modified: | 21 Mar 2024 16:45 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s10474-024-01396-0 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:206883 |