Comment by drdeca

Their notation of “ K_{ℱ_{QG}}” wasn’t a problem. Seems a reasonable name for a constant associated with Kolmogorov complexity and a formal system which they’ve named ℱ_{QG}.

The issue is that what they said seemingly was not

"There exists a natural number L such that we can't prove the Kolmogorov complexity of any specific string of bits is more than L."

But

"There exists a natural number L such that we can't prove (in ℱ_{QG}) any statement S whose complexity is more than L.",

which is wrong.

They later go on to say “These strings cannot be generated by programs of length <= n, and hence cannot correspond to provable statements in ℱ_{QG}.” which follows from the previous wrong statement but doesn’t follow from the accurate statement you gave, which seems to suggest that they really did mean the inaccurate statement that they wrote, not the correct one you wrote.