[FOM] Kreisel, Löb, and G2

Aatu Koskensilta Aatu.Koskensilta at uta.fi
Sun Apr 1 19:14:16 EDT 2012

[My apologies to the moderator if this message was posted twice.]

Quoting Panu Raatikainen <panu.raatikainen at helsinki.fi>:

> Apparently the observation that the second incompleteness theorem  
> can be easily derived as a consequence of Löb’s theorem is due to  
> Kreisel...

   Well, that's a triviality, surely. But it was Kreisel who observed  
that Löb's theorem is an immediate consequence of the second  
incompleteness theorem, by considering the theory T' = T + ~A when T  
proves the provability of A to imply A. (Löb's original proof is  
nevertheless of independent interest, of course.)

Aatu Koskensilta (aatu.koskensilta at uta.fi)

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

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