Talk:List of large cardinal properties

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[edit] Note on history of this page

This page was created on 6 November 2005 by cutting and pasting the list part of the article Large cardinal property. To see the history of the list before that date, see the history of Large cardinal property. --Trovatore 05:34, 7 November 2005 (UTC)

[edit] Problem with the list

The consistency strength of zero-dagger is strictly between the existence of one measurable cardinal and the existence of two measurable cardinals. I've modified the list to reflect this. But now of course it's not strictly a list of large cardinal properties anymore; more a list of large cardinal axioms. We should figure out what to do about this. It's the axioms that are linearly ordered by consistency strength. But it's the properties that correspond to articles we want to link to. What's more important, the ordering or the links? We need to decide, or else figure out how to reword things. (Note that this problem is not by any means unique to zero-dagger; for example the λ-supercompact and λ-extendible cardinals interleave, for different values of λ and similarly for n-huge and n-superstrong.) --Trovatore 00:27, 30 November 2005 (UTC)

By the way, apparently it's open (or was open in 2000) whether the consistency strength of the existence of a supercompact is strictly above that of a strong compact. See The Bulletin of Symbolic Logic 6(1):89 (March 2000). --Trovatore 01:20, 30 November 2005 (UTC)

all the axioms should definitely be included. maybe rename the page? Sam Coskey 19:24, 26 October 2006 (UTC)