Answer by Trevor Wilson for Proof of levy forcing and cardinal collapse
In these two cases showing that certain cardinals are collapsed is easier than showing that certain other cardinals aren't collapsed:If $G \subset \text{Col}(\kappa,\lambda)$ is a $V$-generic filter...
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Collapsing a cardinal to $\omega$: $P$ is the set of all finite sequences of ordinals less than a given cardinal $\lambda$. If $\lambda$ is uncountable then forcing with this poset collapses $\lambda$...
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