= Countability of constructible omega-one
{title2=$\mathrm{NC}:\ |\omega_1^L|=\aleph_0$}
This statement says that the <first uncountable ordinal of an inner model> $L$ is a <countable ordinal> in the ambient universe. It can hold together with the <Generalized continuum hypothesis>: start with constructibility and use a <finite-function collapse to countable size> on $\omega_1^L$. The <GCH preservation by a finite-function collapse> calculation gives the relative consistency result already from the consistency of <ZFC>.
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