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Burali-Forti paradox
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(Definition)
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The Burali-Forti paradox demonstrates that the class of all ordinals is not a set. If there were a set of all ordinals,  , then it would follow that  was itself an ordinal, and therefore that
 . Even if sets in general are allowed to contain themselves, ordinals cannot since they are defined so that  is well founded over them.
This paradox is similar to both Russell's paradox and Cantor's paradox, although it predates both. All of these paradoxes prove that a certain object is “too large” to be a set.
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"Burali-Forti paradox" is owned by Henry.
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Cross-references: object, Cantor's paradox, Russell's paradox, similar, contain, ordinals, class, paradox
There are 3 references to this entry.
This is version 5 of Burali-Forti paradox, born on 2002-09-28, modified 2006-08-16.
Object id is 3484, canonical name is BuraliFortiParadox.
Accessed 3679 times total.
Classification:
| AMS MSC: | 03-00 (Mathematical logic and foundations :: General reference works ) |
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Pending Errata and Addenda
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