Rank-into-rank

1. There is a nontrivial elementary embedding of V_λ into itself.
2. There is a nontrivial elementary embedding of V into a transitive class M that includes V_λ where λ is the first fixed point above the critical point.
3. There is a nontrivial elementary embedding of V_λ+1 into itself.
4. There is a nontrivial elementary embedding of L(V_λ+1 ) into itself with the critical point below λ.

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