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asked Sep 8 at 9:17

Is $2^{|X|} = \aleph_{|X|^+}$ for all infinite sets $X$ consistent with ZFC?

Is $2^{|X|} = \aleph_{|X|^+}$ for all infinite sets $X$ consistent with ZFC? If not, is there a proper class of cardinalities $|X|$ of sets $X$ for which this is consistent with ZFC?

For a point of reference, see Can the continuum be a singular cardinal?

set-theory

asked Sep 8 at 9:17

Jesse Elliott