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Results tagged with forcing
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user 103802
Forcing is a method first used to prove the continuum hypothesis is independent of the classical axioms of set theory
11
votes
Forcing notions adding minimal reals
Splitting forcing is a little-known forcing that adds a splitting real and creates a minimal extension. It consists of splitting trees ordered by inclusion. … In my recent preprint (arxiv link), I show that splitting forcing adds a minimal real (Corollary 4.20) and provide part of an argument for the minimality of the forcing extension (Corrolary 3.21). …
8
votes
1
answer
519
views
Intersection of two generic extensions
But this example looks fairly complicated and I am wondering whether this is already the case for Cohen forcing, i.e:
Can we find two Cohen reals $c_0$, $c_1$ over $M$ so that $M[c_0] \cap M[c_1]$ is …
2
votes
Independent families of functions on $\omega$ of size continuum
For (d) maybe the following was meant:
Take your independent family $F$ and partition it into continuum many families of size $\omega$:
$F = \{ I_{\alpha,n} : \alpha< \mathfrak{c},n \in \omega \}$ …