Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
From: Josh Purinton (usenet-noreply.a.jp_at_xoxy.net)
Date: 01/12/05
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Date: 12 Jan 2005 01:33:34 GMT
In article <41e46743$0$575$b45e6eb0@senator-bedfellow.mit.edu>,
<tchow@lsa.umich.edu> wrote:
>PRA isn't strong enough to prove Goedel's theorems, for example.
According to Shankar's _ Mathematics, Machines, and Goedel's Proof _;
``Goedel's incompleteness theorem represents a significant landmark in
mathematics. [...] Feferman [Fe82] has shown that the incompleteness
proof can be carried out within PRA.'' (page 141)
[Fe82] S. Feferman. Inductively presented systems and the formalization of
mathematics. In D. van Dalen, D. Lascar, and J. Smiley, editors, _ Logic
Colloquium '80 _. North-Holland, Amsterdam, 1982.
-- Josh Purinton
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