Timeline for Ultrafilters arising from Keisler-Shelah ultrapower characterisation of elementary equivalence
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 16, 2010 at 2:17 | comment | added | Joel David Hamkins | My current understanding of the history of the Keisler-Shelah theorem is that Keisler proved it under GCH using the arguments I have mentioned, and Shelah removed the need for GCH. | |
| May 14, 2010 at 19:46 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
added 426 characters in body; edited body; added 4 characters in body
|
| May 13, 2010 at 23:45 | comment | added | Grant Olney Passmore | Ah beautiful! And thank you for suggesting the Rudin-Keisler order + pointing out that equivalence. Again, this is very helpful. | |
| May 13, 2010 at 22:37 | comment | added | Joel David Hamkins | I've realized that the saturation+back-and-forth argument also gives you a quick proof of your instance of the Keisler-Shelah theorem in the case that CH holds, since the two ultrapowers will be elementary equivalent and saturated of size continuum. When CH fails, I'm not sure what happens, but the class of ultrafilters is intensely studied. The Rudin-Keisler order is equivalent to commutative diagrams factoring the ultrapower maps, so this may interest you. | |
| May 13, 2010 at 21:56 | comment | added | Grant Olney Passmore | I'm very interested in the not-CH case as well, though the question seems like it might be difficult. If we do eventually get a nice answer for the set of solutions in the context of not-CH, what is your feeling on the right machinery for examining structure in the solution space? Is the Rudin-Blass ordering on ultrafilters here the standard machinery? | |
| May 13, 2010 at 21:03 | comment | added | Joel David Hamkins | Thanks for accepting. Meanwhile, I'd still like to hear how flexible the choice of U is when CH fails... | |
| May 13, 2010 at 20:55 | vote | accept | Grant Olney Passmore | ||
| May 13, 2010 at 20:55 | comment | added | Grant Olney Passmore | This is so helpful, thanks so much! | |
| May 13, 2010 at 20:18 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
added 78 characters in body
|
| May 13, 2010 at 20:12 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |