Let $\kappa$ be a supercompact cardinal. Then there exists a function $\ell:\kappa\to V_\kappa$ such that for every set $a$ and every cardinal $\theta$ with $a\in V_\theta$, there is a $\theta$-supercompactness embedding $j:V\to M$ such that
\begin{align*}
j(\ell)(\kappa)=a.
\end{align*}
Knowledge Status
Discrete MathematicsSet Theory
Discussion
A large-cardinal result from Set Theory III concerning laver function theorem for supercompact cardinals, used to organize the hierarchy of reflection, embeddings, determinacy, and consistency strength.
Proof under construction
Proof under construction
A complete reviewed proof has not been accepted yet.