Talk:Miner's Cardinal/@comment-36856644-20181022141650/@comment-39162-20181103000935

There is, though to my understanding that's just a nerdy joke.

Essentially, cardinals are arranged by consistency strength - if you have two large cardinals, say X and Y, then X is said to be stronger than Y if ZFC+X can prove that ZFC+Y is consistent. Large cardinals happen to all be nicely ordered by this, as far as we can tell.

1=0, then, is a very strong axiom indeed - in fact, ZFC+(1=0) can prove everything consistent, because it's a contradiction!