= Lusin set construction under CH
{c}
{title2=$A=\{x_\alpha:\alpha<\omega_1\}$}
Under the <Continuum hypothesis>, enumerate the meagre $F_\sigma$ covers by $\omega_1$. At stage $\alpha$ choose a new real outside all earlier covers and the previous choices. The excluded union is meagre, so the <Baire category theorem> makes the choice possible. Each cover then contains only countably many selected points. Arbitrary <meagre sets> need not themselves have only continuum many possible choices; the coded covers are what is enumerated.
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