Definitions

Superstrong cardinal

In mathematics, a cardinal number κ is called superstrong if and only if there exists an elementary embedding j : VM from V into a transitive inner model M with critical point κ and $V_\left\{j\left(kappa\right)\right\}$M.

Similarly, a cardinal κ is n-superstrong if and only if there exists an elementary embedding j : VM from V into a transitive inner model M with critical point κ and $V_\left\{j^n\left(kappa\right)\right\}$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

• Kanamori, Akihiro (2003). The Higher Infinite : Large Cardinals in Set Theory from Their Beginnings. 2nd ed, Springer. ISBN 3-540-00384-3.

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