= Keisler extension property
{c}
An inaccessible cardinal $\kappa$ has the Keisler extension property when there is a proper <transitive set> $X\supsetneq V_\kappa$ for which
$$
(V_\kappa,\in)\prec(X,\in).
$$
Such a $\kappa$ is not the least inaccessible cardinal: $X$ regards $\kappa$ as inaccessible, <elementary substructure>[elementarity] reflects the existence of an inaccessible into $V_\kappa$, and <strong-inaccessibility absoluteness from rank agreement> makes the resulting witness genuinely inaccessible below $\kappa$.
Back to article page
