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Results tagged with forcing
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user 497904
Forcing is a method first used to prove the continuum hypothesis is independent of the classical axioms of set theory
3
votes
A better way to explain forcing?
Meanwhile, I'm a material set theorist by training and don't want to go so far as advertising topos-theoretic forcing (at least before I understand how iterated forcing works in that setting), so let me … Now we can talk about forcing. Say we want to create a model of $\mathsf{ZFC}+\lnot\mathsf{CH}$. …
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9
votes
0
answers
250
views
Naive way to violate $\mathsf{SCH}$ at $\aleph_\omega$
The usual way to get the failure of $\mathsf{SCH}$ at $\aleph_\omega$ is to start with a suitable model with a large cardinal $\kappa$ satisfying $2^\kappa=\kappa^{++}$, and then force with "Prikry forcing … A more naive approach would be ordinary Prikry forcing followed by a (full support) product or iteration of Levy collapses. Is there absolutely zero chance for this to work? …
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11
votes
3
answers
785
views
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 co …
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