The Morris model

Karagila, Asaf (2020) The Morris model. Proceedings of the American Mathematical Society, 148 (3). pp. 1311-1323. ISSN 0002-9939

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Abstract

Douglass B. Morris announced in 1970 that it is consistent with ZF that "For every α, there exists a set Aα which is the countable union of countable sets, and P(Aα) can be partitioned into ℵα non-empty sets". The result was never published in a journal, and seems to have been lost, save a mention in Jech's "Axiom of Choice". We provide a proof using modern tools derived from recent work of the author. We also prove a new preservation theorem for general products of symmetric systems, which we use to obtain the consistency of Dependent Choice with the above statement (replacing "countable union of countable sets" by "union of κ sets of size κ").

Item Type: Article
Uncontrolled Keywords: axiom of choice,symmetric extensions,iterations of symmetric extensions,countable union theorem,applied mathematics,mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600/2604
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 26 Jul 2019 09:30
Last Modified: 13 Jul 2020 23:54
URI: https://ueaeprints.uea.ac.uk/id/eprint/71815
DOI: 10.1090/proc/14770

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