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Forcing is a method first used to prove the continuum hypothesis is independent of the classical axioms of set theory
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Two versions of "absolutely ccc"
In the paper, Shelah says that a forcing notion $\mathcal{P}$ is absolutely ccc if it remains ccc after forcing with any ccc notion. … Elsewhere, I have seen it defined that a forcing notion $\mathcal{P}$ is absolutely ccc if it remains ccc after any forcing. (This would be indestructibly ccc from Bartoszyński-Judah.) …