PlanetMath: successor cardinal

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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 1667 times total.

Classification:

AMS MSC:

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

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