Talk:Metatheorem

The single example in this article seems atypical from the point of view of mathematical logic. In any case, there are probably many good examples that could be included. --Quux0r 08:29, 16 April 2007 (UTC)

Metalogic
Even under Arthur Rubin's conservative view that nothing belongs under the metalogic category, one would have to accept that a metatheorem of logic is a theorem of metalogic. It is appropriately in the category metalogic. Pontiff Greg Bard (talk) 18:59, 17 January 2008 (UTC)
 * Ah, but a "metatheorem" is not (at least necessarily) a "metatheorem of logic". I still don't think it fits, but I won't fight about it.  &mdash; Arthur Rubin |  (talk) 20:03, 17 January 2008 (UTC)

About theorems
Not all metatheorems are theorems "about theorems". For example, the theorem that T = "second-order Peano arithmetic" has only one model is certainly a metatheorem, since this is not provable in T but is a theorem about T provable in the metatheory. But this theorem does not refer in any way to provability in T, so it is not in any sense a theorem "about theorems". &mdash; Carl (CBM · talk) 22:39, 17 September 2009 (UTC)