# Questions tagged [forcing]

Forcing is a method first used to prove the continuum hypothesis is independent of the classical axioms of set theory

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### Countable closure of quotient forcing

Let us say that a partial order is "countably closed with infima" if every descending $\omega$-sequence has an infimum. Suppose $P$ and $Q$ are posets that are countably closed with infima, ...
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### When are two forcing posets "the same"?

Let $B$ and $C$ be complete Boolean algebras. To avoid triviality I may also want them to be atomless. For $b\in B$ nonzero, denote $B\upharpoonright b=\{p\in B:p\leq b\}$, which can be viewed as a ...
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### Uniformization of almost disjoint families

Suppose $\mathcal{F} \subseteq \mathcal{P} (\omega)$ is an almost disjoint family and $\aleph_0 < \vert \mathcal{F} \vert = \kappa < 2^{\aleph_0}$. Is it consistent that for some such cardinal ...
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### $\mathtt{PSP}$ holding only for sets of cardinality $\mathfrak{c}$

Consider the sentence $\mathtt{PSP}_\mathfrak{c}$: "Every subset of $\mathbb{R}$ having the cardinality of the continuum contains a Cantor set". A priori this sentence is weaker than the ...
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