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Large cardinal
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==Partial definition== A necessary condition for a property of cardinal numbers to be a ''large cardinal property'' is that the existence of such a cardinal is not known to be inconsistent with [[ZFC|ZF]] and that such a cardinal ''Ξ''<!--Kappa--> would be an uncountable initial ordinal for which [[constructible universe|''L''<sub>''Ξ''</sub>]]<!--Kappa--> is a model of ZFC. If ZFC is [[consistent]], then ZFC does ''not'' imply that any such large cardinals exist.
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