Timeline for What are some examples of subtle logical pitfalls?
Current License: CC BY-SA 3.0
7 events
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| May 24, 2013 at 1:18 | comment | added | Asaf Karagila♦ | @Carl: And half the crazy non-AC results are merely standard use of permutations to carry partial structure, but not the AC-induced substructure. That doesn't make things less amazing or lovable! :-) | |
| May 24, 2013 at 1:15 | comment | added | Carl Mummert | @Asaf: that result is pretty, but it is a standard sort of overspill argument | |
| May 23, 2013 at 12:49 | comment | added | Asaf Karagila♦ | @Zhen Lin: This is one of the most confusing theorems I've seen ever. I love it! | |
| May 23, 2013 at 12:48 | comment | added | Zhen Lin | Actually, the construction of JDH indicated here shows that Fact I is enough to construct, within any given model of ZFC, a transitive set that externally is a model of ZFC! | |
| May 23, 2013 at 12:33 | comment | added | Carl Mummert | Part of the reason for this confusion, I am sorry to say, is that set theorists are often not very clear about the metatheory/object theory distinction in their writing. (Of course I have some bias about this from working with proof theory.) The confusion with point 1 could be avoided by writing "for every metafinite subset $S$ of the ZFC axioms, ZFC proves that $S$ has a model". | |
| May 23, 2013 at 12:28 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 | added 13 characters in body |
| May 23, 2013 at 4:25 | history | answered | Asaf Karagila♦ | CC BY-SA 3.0 |