  Chaitin's incompleteness theorem states that sufficiently rich formal systems
cannot prove lower bounds on Kolmogorov complexity. In this paper we extend
this theorem by showing theories that prove the Kolmogorov complexity of a
large (but finite) number of strings are inaccessible. This is done by first
showing such theories have large information with the halting sequence. Then,
by applying the independence postulate, such theories are shown to be
inaccessible in the physical world.
