[FOM] Inconsistency of P

Daniel Mehkeri dmehkeri at gmail.com
Sun Oct 2 12:48:40 EDT 2011

 > Now as Tao correctly notes later (let us fix an arithmetization), a
 > relatively simple theory T may have a subtheory S which has an
 > astronomically large Kolmogorov complexity.
 > But of course, being a subtheory, it cannot prove more cases of
 > K(n) > m than T. So the minimal “characteristic” constant of S cannot
 > be larger than that of T.
 > So Tao’s original claim, that “Basically, in order for Chaitin’s
 > theorem (10) to hold, the Kolmogorov complexity of the consistent
 > theory T has to be less than l ” is false, or at least ambiguous and
 > unclear.

Yes. To quickly clarify: as I understood it, the proof attempt was 
relying on the fact that if T proves K(n)>m, then T is inconsistent. If 
a subtheory of T proves K(n)>m, then it does not follow that the 
subhteory is inconsistent.

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