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.Axiom I3: There is a nontrivial elementary embedding of into itself. Axiom I2: There is a nontrivial elementary embedding of into a transitive class that includes where is the first fixed point above the critical point. Axiom I1: There is a nontrivial elementary embedding of into itself. Axiom I0: There is a nontrivial elementary embedding of into itself with critical point below .

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