Rank-into-rank

In set theory, a branch of mathematics, a rank-into-rank embedding is a large cardinal property defined by one of the following four axioms given in order of increasing consistency strength. (A set of rank < λ is one of the elements of the set Vλ of the von Neumann hierarchy.) These are essentially the strongest known large cardinal axioms not known to be inconsistent in ZFC; the axiom for Reinhardt cardinals is stronger, but is not consistent with the axiom of choice. Every I0 cardinal κ (speaking here of the critical point of j) is an I1 cardinal.

Rank-into-rank

In set theory, a branch of mathematics, a rank-into-rank embedding is a large cardinal property defined by one of the following four axioms given in order of increasing consistency strength. (A set of rank < λ is one of the elements of the set Vλ of the von Neumann hierarchy.) These are essentially the strongest known large cardinal axioms not known to be inconsistent in ZFC; the axiom for Reinhardt cardinals is stronger, but is not consistent with the axiom of choice. Every I0 cardinal κ (speaking here of the critical point of j) is an I1 cardinal.