Also a bitstring might be random/incompressible in reference to a Turing machine, but become compressible in reference to a halting oracle. E.g. "list the Nth

Also a bitstring might be random/incompressible in reference to a Turing machine, but become compressible in reference to a halting oracle. E.g. "list the Nth Turing incompressible bitstring" is possible with a halting oracle, so for some N and S it is the case that log2(N) < len(S) and thus S is compressible with regard to a halting oracle but not with regard to a Turing machine.