Talk:Cardinal
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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 "Cardinal" has a pretty well-defined religious meaning as well, and "cardinal number" is not outdated.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