cousin_it comments on No one knows what Peano arithmetic doesn't know - Less Wrong

17 Post author: cousin_it 16 December 2011 09:36PM

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Comment author: cousin_it 17 December 2011 02:06:14AM 0 points [-]

For your final question, I find it hard to imagine a notion of "formal system" that does not just mean "language."

How about http://en.wikipedia.org/wiki/First-order_logic#Syntax ?

Comment author: Douglas_Knight 17 December 2011 02:17:13AM *  0 points [-]

So you agree that "provability oracle for an RE formal system" is the same as "membership oracle for an RE language" and your question is trivial?

ETA: No, first order languages does restrict the set of languages. But I object to this usage. "Formal systems" should include more general systems.

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