Talk:Rank into rank

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There is (or rather, I have) some confusion over the terminology "$\omega$-huge". I have heard Kunen's Inconsistency described as a proof that there is no $\omega$-huge cardinal, but Woodin uses the term to refer to the critical point of these strong embeddings. What's the understanding of the community? Devilsstaircase 22:28, 11 January 2012 (PST)