Аннотации:
We prove a completeness criterion for quasi-reducibility and generalize it to higher levels of the arithmetical hierarchy. As an application of the criterion we obtain Q-completeness of the set of all pairs (x, n) such that the prefix-free Kolmogorov complexity of x is less than n. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA.