Timeline for Interesting examples of countable support iteration of ccc forcings

7 events

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Jan 6, 2018 at 19:33	comment	added	Not Mike		@IianSmythe Thank you for clearing up my confusion.
Dec 30, 2017 at 15:09	comment	added	Jing Zhang		I wouldn't call such iterations "uninteresting". Miyamoto's thesis may have results along these lines. In particular, I think he showed the countable support iteration of Cohen forcing of weakly compact length forces $\omega_2$ has the tree property.
Dec 29, 2017 at 0:48	comment	added	Iian Smythe		@NotMike If $\mathcal{U}$ is a selective ultrafilter, then the restricted Mathias (or Laver) forcing with side conditions in $\mathcal{U}$ is $\sigma$-centered, but does not add Cohen reals. See, e.g.: mathoverflow.net/questions/96930/…. These are the sorts of forcings I'm thinking about.
Dec 28, 2017 at 21:41	comment	added	Not Mike		Don't $\sigma$-centered po-sets always add a Cohen? Or is that an open question? I vaugely remember something about the existence of a certain type of ultrafilter being required.
S Dec 28, 2017 at 16:35	history	suggested	Santi Spadaro		Added a tag
Dec 28, 2017 at 16:09	review	Suggested edits
S Dec 28, 2017 at 16:35
Dec 27, 2017 at 18:30	history	asked	Iian Smythe	CC BY-SA 3.0