Timeline for What is the general opinion on the Generalized Continuum Hypothesis?
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2010 at 17:45 | comment | added | François G. Dorais | @Harry: There is no fixed point. The usual way to get these forcing principles will preserve GCH from some point on. | |
| Feb 11, 2010 at 17:15 | comment | added | Harry Gindi | @François: If we take ZFC+MM, at what point does GCH "come into effect", as it were? | |
| Feb 7, 2010 at 17:39 | comment | added | François G. Dorais | @Justin: However, you're completely right that I shouldn't have said that PFA and MM are "very local" since at the heart of their local nature is a very global reflection principle. | |
| Feb 7, 2010 at 14:02 | comment | added | François G. Dorais | @Justin: Wouldn't the failure of SCH be a drastic event by itself? (I always thought Viale's result was easier to understand in the contrapositive.) | |
| Feb 7, 2010 at 3:39 | comment | added | Harry Gindi | .. GCH => SCH... | |
| Feb 7, 2010 at 3:05 | comment | added | Justin Palumbo | @francois: PFA implies the singular cardinal hypothesis, which is saying it has pretty drastic effects even above the continuum | |
| Feb 7, 2010 at 2:07 | comment | added | François G. Dorais | @Haim: I don't have much of a personal opinion. My answer should not be taken too seriously, but it does match what I've been hearing (from Berkeley and elsewhere) over time... | |
| Feb 6, 2010 at 21:57 | comment | added | Haim | I thought that Woodin's recent work has moved the Berkeley continuum meter away from Aleph_1, but I may be wrong. This kind of stuff is not very popular in my place. :( | |
| Feb 6, 2010 at 2:28 | comment | added | Harry Gindi | I don't know, something like a "best of both worlds" sort of scenario? | |
| Feb 6, 2010 at 2:11 | comment | added | François G. Dorais | A solution to what? | |
| Feb 6, 2010 at 2:09 | comment | added | Harry Gindi | Why doesn't it appear to be necessary? Isn't having MM+(GCH-S), where S is some bounded set of a cardinals an optimal solution? | |
| Feb 6, 2010 at 2:04 | comment | added | François G. Dorais | Forcing axioms such as MA, PFA, and even MM are very local and they don't do all that much above the continuum. The usual way of getting them will preserve GCH from some point on, though that does not appear to be necessary. | |
| Feb 6, 2010 at 1:50 | comment | added | Harry Gindi | Are the forcing axioms I noted above consistent with any weakened form of the Generalized Continuum Hypothesis? Like, maybe something silly happens for higher cardinals, and it implies GCH for all cardinals not equal to $\aleph_0$ | |
| Feb 6, 2010 at 1:48 | history | answered | François G. Dorais | CC BY-SA 2.5 |