[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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