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Large cardinal property - Wikipedia, the free encyclopedia |
 | | 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 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. |
 | | For example, the existence of a huge cardinal is much stronger, in terms of consistency strength, than the existence of a supercompact cardinal, but assuming both exist, the first huge is smaller than the first supercompact. |
 | | Large cardinals are understood in the context of the von Neumann universe V, which is built up by transfinitely iterating the powerset operation, which collects together all subsets of a given set. |
| en.wikipedia.org /wiki/Large_cardinal (940 words) |
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