Strong-inaccessibility absoluteness from rank agreement
= Strong-inaccessibility absoluteness from rank agreement
If transitive models of enough set theory contain the same $V_{\alpha+1}$, then they agree on whether $\alpha$ is a <strongly inaccessible cardinal>. They have the same subsets and functions on every ordinal below $\alpha$, so they agree on <cardinal number>[cardinality], <regular cardinal>[regularity], and the <strong limit cardinal> property.