Abstract:
A real α is computably enumerable if it is the limit of a computable, increasing,
converging sequence of rationals; α is random if its binary expansion is a random
sequence. Our aim is to offer a self-contained proof, based on the papers [7, 14, 4, 13],
of the following theorem: a real is c.e. and random if and only if it a Chaitin Ω real,
i.e., the halting probability of some universal self-delimiting Turing machine.