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Results tagged with forcing
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user 56878
Forcing is a method first used to prove the continuum hypothesis is independent of the classical axioms of set theory
11
votes
1
answer
705
views
What is the precise relationship between forcing on a poset and the topos of double-negation...
the truth values of the axioms of ZFC are $1$, and the forcing relation can be defined as $p \Vdash \phi$ for $p \in B$ iff the truth value of $\phi$ is at least $p$. … This lets us define a "forcing relation" for $p \in \Omega$ as $p \Vdash' \phi$ iff the terminal map from the Yoneda image of $p$ factors through the truth value of $\phi$. …
- 21.3k
12
votes
3
answers
2k
views
Why do we need a transitive model in forcing arguments?
One major approach to the theory of forcing is to assume that ZFC has a countable transitive model $M \in V$ (where $V$ is the "real" universe). … Can we continue the proof of forcing along these lines? …
- 146