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Can the continuum $\mathfrak c$ be a limit cardinal?

Thanks for any help!

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According to Wiki, I think there are at least two notions of limit cardinals. $\mathfrak c$ seems to be reachable by taking the power set of $\aleph_0$, but not by successor operation without the continuum hypothesis. –  Tunococ Sep 9 '13 at 1:02
    
Related. –  Andres Caicedo Sep 9 '13 at 1:25

1 Answer 1

up vote 5 down vote accepted

Yes. The only restriction is that $\mathfrak{c}$ must be a cardinal of uncountable cofinality. So $\mathfrak{c}$ can be $\aleph_{\omega_1}$, but not $\aleph_\omega$.

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