[FOM] Derivability conditions for Robinson arithmetic
mummertc at marshall.edu
Mon Sep 20 09:42:30 EDT 2010
It's well known that the standard proofs of Goedel's second
incompleteness theorem require that the theory is able to verify the
Hilbert-Bernays derivability conditions for the provability predicate,
or some similar set of derivability conditions. Proofs that Robinson's
arithmetic Q and other weak arithmetics do not prove their own
consistency use different, more ad hoc, methods. Looking through the
literature, I can find various remarks about the derivability
conditions and Q, but nothing specific.
Is there a published proof that one that one of the Hilbert-Bernays
conditions is not provable in Q?
This question was originally posed by Charles Stewart on MathOverflow .
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