Comment by Kranar

Ultimately, I am addressing the original point that was made:

>I think the more correct statement is that there are different models of ZFC in which BB(748) are different numbers.

You asked how this was possible and that's the specific question that I am addressing. As I mentioned elsewhere, to fully appreciate this answer requires parsing some very subtle and nuanced details that simply can not be glossed over or dismissed, if you genuinely want to know how it's possible that ZFC can be consistent even though different models give different values of BB(748).

If you want to argue something else, about what model is correct or what model is incorrect, that's a perfectly fine argument to have but it's more in the realm of philosophy than it is in the realm of formal mathematics.