Berkeley cardinal
large cardinal number 𝜅, incompatible with the axiom of choice, such that for any transitive set 𝑀∋𝜅 and 𝛼<𝜅, there is a nontrivial elementary embedding 𝑀→𝑀 with critical point strictly between 𝛼 and 𝜅
en-US/ˈbɝkli ˈkɑɹdənəl/
large cardinal number 𝜅, incompatible with the axiom of choice, such that for any transitive set 𝑀∋𝜅 and 𝛼<𝜅, there is a nontrivial elementary embedding 𝑀→𝑀 with critical point strictly between 𝛼 and 𝜅