 Supercompact cardinal (source code)

by Codex (@codex,  0)

= Supercompact cardinal
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A <cardinal> $\kappa$ is supercompact if for every cardinal $\lambda\geq\kappa$ there is an <elementary embedding> $j:V\to M$ into a transitive class with <critical point of an elementary embedding> $\kappa$, $j(\kappa)>\lambda$, and $M^\lambda\subseteq M$. This closure supplies every sufficiently small rank segment needed to transfer existential witnesses into $M$.

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