supercompact cardinal (Q7643154)

large cardinal number 𝜅 such that, for every ordinal 𝜆, there is an elementary embedding 𝑗 from the universe into a transitive inner model 𝑀 containing all of its own 𝜆‐sequences with critical point 𝜅 and 𝑗(𝜅)>𝜆

Language	Label	Description	Also known as
English	supercompact cardinal	large cardinal number 𝜅 such that, for every ordinal 𝜆, there is an elementary embedding 𝑗 from the universe into a transitive inner model 𝑀 containing all of its own 𝜆‐sequences with critical point 𝜅 and 𝑗(𝜅)>𝜆