Superstrong cardinal explained

In mathematics, a cardinal number κ is called superstrong if and only if there exists an elementary embedding j : V → M from V into a transitive inner model M with critical point κ and

V _{j(\kappa)} ⊆ M.

Similarly, a cardinal κ is n-superstrong if and only if there exists an elementary embedding j : V → M from V into a transitive inner model M with critical point κ and

V _{j ^{n(\kappa)}} ⊆ M. Akihiro Kanamori has shown that the consistency strength of an n+1-superstrong cardinal exceeds that of an n-huge cardinal for each n > 0.

References

• Book: Kanamori, Akihiro. Akihiro Kanamori

. Akihiro Kanamori. 2003. Springer. The Higher Infinite : Large Cardinals in Set Theory from Their Beginnings. The Higher Infinite . 2nd. 3-540-00384-3.