Talk:Cardinal

The consistency of the existence of strongly inaccessible cardinals can not be proved under ZFC.

Is that correct? I thought the existence of strongly inaccessible cardinals can (provably) not be proved, while

it is open whether their non-existence can be proved.

In other words, "the consistency of the existence of strongly inaccessible cardinals" has not yet been proved

while the consistency of their non-existence has been proved.

Yes, your version is correct. That existence of inacc. cardinals cannot be proved is a direct consequence of the 2nd incompleteness theorem (one observes that the set of all sets with rank less than that of an inacc. cardinal form a model of ZFC).

Incidentally, wouldn't it be better to have the main article at Cardinal number? "Cardinal" has a pretty well-defined religious meaning as well, and "cardinal number" is not outdated.

--AV

not to mention the bird. And the baseball team.--MichaelTinkler

Ok, I'm convinced. Cardinal number it is. --AxelBoldt

As this refers to a subdivision/less obvious definition of the term, could it be emphasised that it is the number that is being referred to, not a religious person being away from their phone (g). Jackiespeel 18:08, 9 January 2006 (UTC)[reply]