Talk:Rank-into-rank

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Regarding the current page contents, would it be safe to say that a cardinal λ is (a) rank-into-rank iff it satisfies one of the four axioms? (which?) -- Schnee 11:54, 18 Dec 2003 (UTC)

Since I think that large cardinal properties which involve elementary embeddings belong to their critical points, I would call κ a rank-into-rank cardinal iff it is the critical point of any of the elementary embeddings mentioned in the definitions of I3, I2, I1, or I0. λ is larger than κ, but it is not as strong a limit, in fact, it has cofinality ω. JRSpriggs 05:58, 6 May 2006 (UTC)

[edit] Elementary Embedding Of V_λ For Non-Inaccessible λ?

The article mentions elementary embeddings of V_λ but also says that λ cannot be inaccessible(assuming choice). But an elementary embedding is an isomorphism between models, so if λ isn't inaccessible, what exactly is V_λ being considered as a model of?

10:39, 6 August 2007 (UTC)