Résumé
Assume that a tuple of binary strings (a) over bar = < a(1), ..., a(n)> has negligible mutual information with another string b. Does this mean that properties of the Kolmogorov complexity of (a) over bar do not change significantly if we relativize them to b? This question becomes very nontrivial when we try to formalize it. In this paper we investigate this problem for a special class of properties (for properties that can be expressed by an there exists-formula). In particular, we show that a random (conditional on (a) over bar) oracle b does not help to extract common information from the strings a(i).