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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 $\phi$. …
dorebell's user avatar
  • 3,058
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? …
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