Is it possible to get rid of the small correction terms such as in Theorem 5.3? Note that the construction in the proof shows that is actually bounded by , the complexity of the c.e. number with minimal . The facts , , , as well as intuition and wishful thinking inspired by Shannon-Fano Theorem [38] and Coding Theorem 5.1 suggest there might indeed be tighter bounds:

Juergen Schmidhuber 2003-02-13