The study of sets is important and thus popular in the business and economic world for three major reasons: Basic understanding of concepts in sets and set algebra provides a form of logical language… Expand

We show that a set is 2-random if and only if there is a constant c such that infinitely many initial segments x of the set are c-incompressible: C(x) ≥ ∣x∣ − c.Expand

AbstractLet R be a notion of algorithmic randomness for individual subsets of ℕ. A set B is a base for R randomness if there is a Z ≥ T B such that Z is R random relative to B. We show that the bases… Expand

We introduce the concepts of complex and autocomplex sets, where a set A is complex if there is a recursive, nondecreasing and unbounded lower bound on the Kolmogorov complexity of the prefixes (of the characteristic sequence) of A, and Autocomplex is defined likewise with recursive replaced by A-recursive.Expand

We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr trivials based on truth-table reducibility.Expand