Given two transitive models of ZFC, is there a way of comparing how "high" the ordinals go in one model versus another?
2026-04-05 20:54:13.1775422453
Comparing how "high" the ordinals go in one model of ZFC versus another.
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Suppose $M_1$ and $M_2$ are two transitive models of ZFC, then $\mathsf{Ord}^{M_1}$ and $\mathsf{Ord}^{M_2}$ are actually two ordinals $\alpha_1$ and $\alpha_2$.
Since those are ordinals, we can compare them and see which one is larger (or if they are equal).