Tall cardinal

In mathematics, a tall cardinal is a large cardinal κ that is θ-tall for all ordinals θ, where a cardinal is called θ-tall if there is an elementary embedding j : V → M with critical point κ such that j(κ) > θ and M^κ ⊆ M.

Tall cardinals are equiconsistent with strong cardinals.

References

• Hamkins, Joel David (2009), "Tall cardinals", Mathematical Logic Quarterly, 55 (1): 68–86, doi:10.1002/malq.200710084, ISSN 0942-5616, MR 2489293, S2CID 19062078