For a deep look at Omega (Chaitin's constant) I'd recommend Chaitin's book Meta Math: The Quest for Omega [1]. A fascinating book. Chaitin has also uploaded th

For a deep look at Omega (Chaitin's constant) I'd recommend Chaitin's book Meta Math: The Quest for Omega [1]. A fascinating book. Chaitin has also uploaded the full text (pdf) of the book to Arxiv.org [2]. [1] http://www.amazon.co.uk/Meta-Maths-Gregory-J-Chaitin/dp/184354525X/ref=sr_1_2?s=books&ie=UTF8&qid=1375795373&sr=1-2 http://www.amazon.co.uk/Meta-Maths-Gregory-J-Chaitin/dp/1843... [2] http://arxiv.org/abs/math/0404335 http://arxiv.org/abs/math/0404335