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Talk:Successor cardinal

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Successor cardinal and Hartogs number

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Isn't the definition provided at the end of current revision (as a definition without AC)

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the same thing as the Hartogs number?

Kompik: Yes, it is. Please sign your contributions to talk with four tildas, e.g. ~~~~. JRSpriggs 03:51, 30 May 2006 (UTC)[reply]

Without choice?

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Do we want to include the following results:

If is any cardinal, then (Hartogs number) is a smallest cardinal m such that (Already included, in part.)

If Dedekind finite, then is the successor cardinal of .

I believe I can show that if is Dedekind infinite, then is a successor cardinal of , but I don't have a reference.

Hence, any cardinal has a successor cardinal. — Arthur Rubin (talk) 18:32, 22 June 2015 (UTC)[reply]