The Bristol model:An abyss called a Cohen real

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Karagila, Asaf ORCID: https://orcid.org/0000-0003-1289-0904 (2018) The Bristol model:An abyss called a Cohen real. Journal of Mathematical Logic, 18 (2). ISSN 0219-0613

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Abstract

We construct a model M of ZF which lies between L and L[c] for a Cohen real c and does not have the form L(x) for any set x. This is loosely based on the unwritten work done in a Bristol workshop about Woodin's HOD Conjecture in 2011. The construction given here allows for a finer analysis of the needed assumptions on the ground models, thus taking us one step closer to understanding models of ZF, and the HOD Conjecture and its relatives. This model also provides a positive answer to a question of Grigorieff about intermediate models of ZF, and we use it to show the failure of Kinna-Wagner Principles in ZF.

Item Type:	Article
Uncontrolled Keywords:	axiom of choice,bristol model,hod conjecture,intermediate models,kinna-wagner principles,symmetric extension,logic ,/dk/atira/pure/subjectarea/asjc/2600/2609
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Logic
Related URLs:	http://www.scopus.com/inward/record.url?... https://arxiv.org/abs/1704.06939
Depositing User:	LivePure Connector
Date Deposited:	16 Apr 2019 08:30
Last Modified:	22 Oct 2022 04:35
URI:	https://ueaeprints.uea.ac.uk/id/eprint/70584
DOI:	10.1142/S0219061318500083

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