Timeline for Number of transitive models of set theory
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Sep 22, 2010 at 3:34 | comment | added | Andrés E. Caicedo | Hi Amit. Yes, unfortunately, in many situations one can actually prove that no model obtained this way is well-founded. There is a tiny hope of doing something similar that actually gives a well-founded structure at the end, by applying Bairwise compactness in some appropriate setting, but at the moment I only see how to make this work starting with large cardinals around the level of measurability. | |
| Sep 22, 2010 at 0:34 | comment | added | Amit Kumar Gupta | Sorry, I wasn't thinking. The model resulting from applying Lowenheim-Skolem will satisfy Foundation but you're right, there's nothing guaranteeing it's well-founded. | |
| Sep 22, 2010 at 0:31 | history | undeleted | Amit Kumar Gupta | ||
| Sep 22, 2010 at 0:30 | history | deleted | Amit Kumar Gupta | ||
| Sep 21, 2010 at 23:36 | comment | added | Joel David Hamkins | Amit, although this argument shows that there will be a proper class of models of ZFC, there is little reason to expect these models to be well-founded, and so you will not get transitive models this way. (In particular, you can only apply the Mostowski collapse to the well-founded models.) | |
| Sep 21, 2010 at 23:27 | history | answered | Amit Kumar Gupta | CC BY-SA 2.5 |