Talk:Metatheorem

Latest comment: 15 years ago by CBM in topic About theorems

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)Reply

Metalogic

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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)Reply

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. — Arthur Rubin | (talk) 20:03, 17 January 2008 (UTC)Reply

About theorems

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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". — Carl (CBM · talk) 22:39, 17 September 2009 (UTC)Reply