Timeline for Why is Cohen's result insufficient to settle CH?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Dec 31, 2010 at 8:01 | comment | added | Zirui Wang | As I read Cohen's result now, I notice it has an assumption, that is ZFC is consistent. Without this assumption, Cohen could have resolved CH. With this assumption, he only showed how to construct a set from an assumed set. Without the assumed set, his method does not work. And Godel showed that no one can construct the assumed set. | |
| Jun 20, 2010 at 18:32 | answer | added | T.. | timeline score: 3 | |
| Jun 20, 2010 at 14:08 | answer | added | Michael Greinecker | timeline score: 3 | |
| Jun 20, 2010 at 12:54 | answer | added | Joel David Hamkins | timeline score: 28 | |
| Jun 20, 2010 at 12:50 | answer | added | Carl Mummert | timeline score: 5 | |
| Jun 20, 2010 at 12:03 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
Corrected spelling and grammar; edited tags
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| Jun 20, 2010 at 11:54 | comment | added | Carl Mummert | The question makes some sense to me, if phrased this way: why doesn't the construction of a model of set theory in which CH let us show that CH fails in the standard model? I don't think that is answered very well (if at all) in the answers to the question Scott Carnahan linked to. I'm not saying it's an extremely deep question, though. (Aside: would someone with the technical ability please edit the question to correct the spelling of "Cohen"? ) | |
| Jun 20, 2010 at 7:05 | comment | added | S. Carnahan♦ | There seem to be several questions on this precise topic already, e.g., mathoverflow.net/questions/10227/… and they have some very well-written answers. Is there something specifically unsatisfying about these answers? | |
| Jun 20, 2010 at 5:34 | comment | added | Gerhard Paseman | I mean, set theory plus this "truth" (and so CH) to hold. Gerhard "Ask Me About System Design" Paseman, 2010.06.19 | |
| Jun 20, 2010 at 5:32 | comment | added | Gerhard Paseman | Cohen showed that (given that there is a model of ZFC) a model can be built in which ZFC holds and CH does not hold. For some, this (along with work of Goedel) settles the issue: ZFC, if it is consistent, does not prove CH. For others, CH is a natural enough condition that, like Euclid's parallel postulate, one wonders if there is some other basic "truth" that should be assumed for set theory to hold. Gerhard "Ask Me About System Design" Paseman, 2010.06.19 | |
| Jun 20, 2010 at 5:06 | history | asked | Zirui Wang | CC BY-SA 2.5 |