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Large cardinal property
In the mathematical field of set theory, a large cardinal property is a property of cardinal numbers, such that the existence of such a cardinal is not known to be inconsistent with ZFC and it has been proven that if ZFC is consistent, then ZFC is consistent with the nonexistence of such a cardinal. Furthermore, unlike the case of the continuum hypothesis, it is (provably) not possible to show that any large cardinal axiom is even consistent with ZFC, from the assumption that ZFC is consistent.
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