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Re: The incompleteness theorems, Sigma-1-completeness, induction, all th

Subject: Re: The incompleteness theorems, Sigma-1-completeness, induction, all that
From: Aatu Koskensilta
Date: Wed, 30 Aug 2006 02:11:48 +0300
Newsgroups: sci.logic
Rupert wrote:
Aatu Koskensilta wrote:
Tbe first incompleteness theorem is usually expressed something like the
following

  For any extension T of Robinson arithmetic we can effectively find a
  sentence G_T, s.t. G_T is true and undecidable in T iff T is
  (1-)consistent.


"If" surely, not "iff"?

To make it "iff", the condition would have to be that T does not prove
its own inconsistency, which is weaker than 1-consistency.

You're right, of course.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
 - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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