= Cardinal fixed point of the singular cardinal enumeration
{title2=$\sigma_\kappa=\kappa$}
There is an uncountable <cardinal number> $\kappa$ with $\sigma_\kappa=\kappa$. Iterate $\kappa_{n+1}=\sigma_{\kappa_n}$ starting with $\aleph_0$. If there is no earlier fixed point, the increasing supremum $\kappa$ has countable <cofinality>, hence is a <singular cardinal>. The <singular cardinal enumeration> is cofinal in $\kappa$ below index $\kappa$, and continuity at this singular supremum gives equality.
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