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Apr 24, 2014 at 22:04 comment added Anton Klyachko @Dan, surely. What you said is basically Metatheorem 3.5.2 from my answer.
Apr 23, 2014 at 21:08 comment added Dan Your theorem order looks strange to me (and OP question too). If $g=1$, clearly, there is a proof of this fact (in every strong enough theory). So, the correct question whether there exists a proof of $g \neq 1$ if $g$ is actually not 1. The answer is - for every particular theory unprovable $g\neq 1$ exists (otherwise we could solve wp). That's all.
Apr 1, 2013 at 10:01 history edited Anton Klyachko CC BY-SA 3.0
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Mar 30, 2013 at 11:13 history answered Anton Klyachko CC BY-SA 3.0