I think the resolution is along the lines of this: * ZFC does not have a unique model that satisfies the axioms. * Each of those models have different "undesc

I think the resolution is along the lines of this: * ZFC does not have a unique model that satisfies the axioms. * Each of those models have different "undescribable numbers" with different properties. But it was a long time I touched model theory, and it was just an optional extra course at uni. https://en.wikipedia.org/wiki/Model_theory https://en.wikipedia.org/wiki/Model_theory