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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?
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?
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?
