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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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votes
Proving results about complete Boolean algebras in ZFC using Boolean valued models
You can, for example, show that many standard complete boolean algebras like Cohen algebra cannot be isomorphic to a quotient $\mathcal{P}(X) / I$ for any sigma ideal $I$ over $X$. These results are d …