Rasiowa–Sikorski lemma
= Rasiowa–Sikorski lemma
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If $M$ is a <countable transitive model>, $\mathbb P\in M$, and $p\in\mathbb P$, enumerate the dense subsets of $\mathbb P$ belonging to $M$ and recursively choose a decreasing sequence starting below $p$ that meets each one. Its upward closure is a <generic filter> over $M$ containing $p$.