tag:blogger.com,1999:blog-3891434218564545511.post5068155987479471482..comments2024-03-27T20:37:09.185-05:00Comments on Alexander Pruss's Blog: Cardinality and Bayesian regularityAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3891434218564545511.post-50153854226090399182012-12-18T12:17:06.099-06:002012-12-18T12:17:06.099-06:00The paper giving this result has just been accepte...The paper giving this result has just been accepted by <i>Philosophy of Science</i>.<br /><br />Yay! Yet another blog post turned into a publication.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-25971529439407418092012-01-13T23:55:05.807-06:002012-01-13T23:55:05.807-06:00Just realized that I only need V to be partially o...Just realized that I only need V to be partially ordered, not totally ordered. Wow.<br /><br />And I can take K* to be just K+.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-48667387035150042912012-01-12T09:21:17.003-06:002012-01-12T09:21:17.003-06:00A formal statement of the no-AC result is this. F...A formal statement of the no-AC result is this. For any cardinality K there is a cardinality K* such that if |X| >= K* and |V| <= K, then a V-probability assignment on the powerset on X is not regular.<br /><br />We can take K* to be K x K+ where K+ is the Hartog's number of K. I got the idea for this from <a href="http://mathoverflow.net/questions/26861/explicit-ordering-on-set-with-larger-cardinality-than-r" rel="nofollow">here</a>.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-1367947502688800402012-01-11T15:41:33.707-06:002012-01-11T15:41:33.707-06:00I can now get similar results without using the Ax...I can now get similar results without using the Axiom of Choice.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.com