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Results tagged with forcing
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user 26705
Forcing is a method first used to prove the continuum hypothesis is independent of the classical axioms of set theory
8
votes
1
answer
333
views
Consistency Strength of "HC is elementary in V[G]"
Let $P$ be the Levy-collapse of the ordinals, so $P$ is a class forcing notion that makes every ordinal countable. …
- 236k
2
votes
Problem understanding a passage of the proof of $\mathfrak{p}=\mathfrak{t}$ involving forcing
Incidentally, the forcing extension is superficial. At the beginning of the proof we can suppose by passing to a Levy collapse that $\mathfrak{t} = 2^{\aleph_0}$. …
- 2,146
5
votes
Accepted
When are generic models not too wild?
For an example of a super-stable theory failing the property, you can take infinitely many unary predicates (so $Th(2^\omega, U_n: n \in \omega)$ where $U_n(\eta)$ holds iff $\eta(n) = 1$). Then if $\ …
- 2,146
3
votes
Accepted
Consistency of Weak Diamond with a Weak Version of Martin's Axiom
So I was looking through related questions on this site and the book "Proper and Improper Forcing" by Shelah kept popping up. So I checked it out and the appendix actually resolves the question. … This proof is gleaned from the proof of Theorem 2.11 in the Appendix of Shelah's "Proper and Improper forcing." …
- 2,146
6
votes
1
answer
387
views
Consistency of Weak Diamond with a Weak Version of Martin's Axiom
For all I know, both of these forcing extensions witness the consistency of $\Phi^* \land MA^*$. …
- 2,146