For every ccc partial ordering \(P\) and every set \(\{ D_\alpha :\alpha &lt;\omega_1\}\) of dense subsets of \(P\), there exists a filter \(G\subseteq P\) that is generic for the set, i.e., \(G\cap D_\alpha \ne {\varnothing}\), for all \(\alpha &lt;\omega_1\).