FOM: request for info

Sam Buss sbuss at
Fri Feb 12 15:19:24 EST 1999

  The equivalence of a Godel sentence for S and the statement
Con(S)  can be proved in either:  (for "reasonable systems" S)

	a) I-Delta_0+\Omega_1    (in a paper of Paris & Wilkie, see 
				  also work of Ed Nelson)
	b) S^1_2	 (slightly later in my phd thesis).

As far as I know, these are the weakest systems in which the
G\"odel incompleteness theorem has been proved in an
manner which is *intensional* in the sense of Feferman.
  If there are any other intensional proofs the second 
incompleteness theorem in weak systems, I'd be interested 
to hear about them.

 --- Sam Buss

In reply to:
> Date: Fri, 12 Feb 1999 11:15:51 -0500 (EST)
> From: Neil Tennant <neilt at>
> To: fom at
> Subject: FOM: request for info> Cc: neilt at
> Can anyone tell me what the weakest theory of arithmetic is within which
> one can formalize the argument for the equivalence of the G"odel-sentencefor S with Con(S), where S contains Robinson's arithmetic R and S is a 
> subtheory of Th(N)?
> Neil Tennant

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