Authors: | Farah, Ilijas Veličković, Boban |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Von Neumann's problem and large cardinals | Journal: | Bulletin of the London Mathematical Society | Volume: | 38 | Issue: | 6 | First page: | 907 | Last page: | 912 | Issue Date: | 1-Jan-2006 | Rank: | M22 | ISSN: | 0024-6093 | DOI: | 10.1112/S0024609306018704 | Abstract: | It is a well-known problem of Von Neumann to discover whether the countable chain condition and weak distributivity of a complete Boolean algebra imply that it carries a strictly positive probability measure. It was shown recently by Balcar, Jech and Pazák, and by Veličković, that it is consistent with ZFC, modulo the consistency of a supercompact cardinal, that every ccc weakly distributive complete Boolean algebra carries a contiuous strictly positive submeasure - that is, it is a Maharam algebra. We use some ideas of Gitik and Shelah and implications from the inner model theory to show that some large cardinal assumptions are necessary for this result. |
Publisher: | London Mathematical Society |
Show full item record
SCOPUSTM
Citations
5
checked on Oct 17, 2024
Page view(s)
9
checked on Oct 17, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.