Rank into rank cardinals seem to push the limits of consistency, and are stronger than (almost?) every other consistent large cardinal. Despite that, It seems to me, and from a few online discussion posts I've seen, that large cardinals should go on "forever." How would one go beyond rank into rank? Would it require a method other than elementary embeddings? Have any stronger axioms (which have not been found inconsistent) been formulated?
2026-03-30 15:44:24.1774885464
How would one formulate large cardinals beyond rank into rank?
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