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[parent] successor cardinal (Definition)

A successor cardinal is a cardinal that is the cardinal successor of some cardinal.

Every finite cardinal other than $0$ is a successor cardinal. An infinite cardinal $\aleph_\alpha$ is a successor cardinal if and only if $\alpha$ is a successor ordinal.



"successor cardinal" is owned by yark.
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See Also: limit cardinal, cardinal successor


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Cross-references: successor ordinal, infinite, finite, cardinal successor, cardinal
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This is version 3 of successor cardinal, born on 2003-12-01, modified 2007-01-07.
Object id is 5440, canonical name is SuccessorCardinal.
Accessed 2034 times total.

Classification:
AMS MSC: 03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers)
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